An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox
Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly prop...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kastner, Felix [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2022 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2022 |
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| Übergeordnetes Werk: |
Enthalten in: Numerical algorithms - Bussum : Baltzer, 1991, 93(2022), 1 vom: 12. Dez., Seite 27-66 |
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| Übergeordnetes Werk: |
volume:93 ; year:2022 ; number:1 ; day:12 ; month:12 ; pages:27-66 |
| Links: |
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| DOI / URN: |
10.1007/s11075-022-01401-z |
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| Katalog-ID: |
SPR049967908 |
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| 100 | 1 | |a Kastner, Felix |e verfasserin |0 (orcid)0000-0003-0504-6211 |4 aut | |
| 245 | 1 | 3 | |a An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox |
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| 520 | |a Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. | ||
| 650 | 4 | |a Iterated stochastic integral |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Lévy area |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stochastic simulation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Julia |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Software toolbox |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stochastic differential equation |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Stochastic partial differential equation |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Rößler, Andreas |0 (orcid)0000-0002-2740-2697 |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Numerical algorithms |d Bussum : Baltzer, 1991 |g 93(2022), 1 vom: 12. Dez., Seite 27-66 |w (DE-627)318468581 |w (DE-600)2002650-X |x 1572-9265 |7 nnns |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s11075-022-01401-z |z kostenfrei |3 Volltext |
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10.1007/s11075-022-01401-z doi (DE-627)SPR049967908 (SPR)s11075-022-01401-z-e DE-627 ger DE-627 rakwb eng Kastner, Felix verfasserin (orcid)0000-0003-0504-6211 aut An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. Iterated stochastic integral (dpeaa)DE-He213 Lévy area (dpeaa)DE-He213 Stochastic simulation (dpeaa)DE-He213 Julia (dpeaa)DE-He213 Software toolbox (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Stochastic partial differential equation (dpeaa)DE-He213 Rößler, Andreas (orcid)0000-0002-2740-2697 aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 93(2022), 1 vom: 12. Dez., Seite 27-66 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:93 year:2022 number:1 day:12 month:12 pages:27-66 https://dx.doi.org/10.1007/s11075-022-01401-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 93 2022 1 12 12 27-66 |
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10.1007/s11075-022-01401-z doi (DE-627)SPR049967908 (SPR)s11075-022-01401-z-e DE-627 ger DE-627 rakwb eng Kastner, Felix verfasserin (orcid)0000-0003-0504-6211 aut An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. Iterated stochastic integral (dpeaa)DE-He213 Lévy area (dpeaa)DE-He213 Stochastic simulation (dpeaa)DE-He213 Julia (dpeaa)DE-He213 Software toolbox (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Stochastic partial differential equation (dpeaa)DE-He213 Rößler, Andreas (orcid)0000-0002-2740-2697 aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 93(2022), 1 vom: 12. Dez., Seite 27-66 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:93 year:2022 number:1 day:12 month:12 pages:27-66 https://dx.doi.org/10.1007/s11075-022-01401-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 93 2022 1 12 12 27-66 |
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10.1007/s11075-022-01401-z doi (DE-627)SPR049967908 (SPR)s11075-022-01401-z-e DE-627 ger DE-627 rakwb eng Kastner, Felix verfasserin (orcid)0000-0003-0504-6211 aut An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. Iterated stochastic integral (dpeaa)DE-He213 Lévy area (dpeaa)DE-He213 Stochastic simulation (dpeaa)DE-He213 Julia (dpeaa)DE-He213 Software toolbox (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Stochastic partial differential equation (dpeaa)DE-He213 Rößler, Andreas (orcid)0000-0002-2740-2697 aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 93(2022), 1 vom: 12. Dez., Seite 27-66 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:93 year:2022 number:1 day:12 month:12 pages:27-66 https://dx.doi.org/10.1007/s11075-022-01401-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 93 2022 1 12 12 27-66 |
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10.1007/s11075-022-01401-z doi (DE-627)SPR049967908 (SPR)s11075-022-01401-z-e DE-627 ger DE-627 rakwb eng Kastner, Felix verfasserin (orcid)0000-0003-0504-6211 aut An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. Iterated stochastic integral (dpeaa)DE-He213 Lévy area (dpeaa)DE-He213 Stochastic simulation (dpeaa)DE-He213 Julia (dpeaa)DE-He213 Software toolbox (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Stochastic partial differential equation (dpeaa)DE-He213 Rößler, Andreas (orcid)0000-0002-2740-2697 aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 93(2022), 1 vom: 12. Dez., Seite 27-66 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:93 year:2022 number:1 day:12 month:12 pages:27-66 https://dx.doi.org/10.1007/s11075-022-01401-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 93 2022 1 12 12 27-66 |
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10.1007/s11075-022-01401-z doi (DE-627)SPR049967908 (SPR)s11075-022-01401-z-e DE-627 ger DE-627 rakwb eng Kastner, Felix verfasserin (orcid)0000-0003-0504-6211 aut An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2022 Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. Iterated stochastic integral (dpeaa)DE-He213 Lévy area (dpeaa)DE-He213 Stochastic simulation (dpeaa)DE-He213 Julia (dpeaa)DE-He213 Software toolbox (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Stochastic partial differential equation (dpeaa)DE-He213 Rößler, Andreas (orcid)0000-0002-2740-2697 aut Enthalten in Numerical algorithms Bussum : Baltzer, 1991 93(2022), 1 vom: 12. Dez., Seite 27-66 (DE-627)318468581 (DE-600)2002650-X 1572-9265 nnns volume:93 year:2022 number:1 day:12 month:12 pages:27-66 https://dx.doi.org/10.1007/s11075-022-01401-z kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 93 2022 1 12 12 27-66 |
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Enthalten in Numerical algorithms 93(2022), 1 vom: 12. Dez., Seite 27-66 volume:93 year:2022 number:1 day:12 month:12 pages:27-66 |
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Enthalten in Numerical algorithms 93(2022), 1 vom: 12. Dez., Seite 27-66 volume:93 year:2022 number:1 day:12 month:12 pages:27-66 |
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Iterated stochastic integral Lévy area Stochastic simulation Julia Software toolbox Stochastic differential equation Stochastic partial differential equation |
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Numerical algorithms |
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Kastner, Felix @@aut@@ Rößler, Andreas @@aut@@ |
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Kastner, Felix |
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Kastner, Felix misc Iterated stochastic integral misc Lévy area misc Stochastic simulation misc Julia misc Software toolbox misc Stochastic differential equation misc Stochastic partial differential equation An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox |
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An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox Iterated stochastic integral (dpeaa)DE-He213 Lévy area (dpeaa)DE-He213 Stochastic simulation (dpeaa)DE-He213 Julia (dpeaa)DE-He213 Software toolbox (dpeaa)DE-He213 Stochastic differential equation (dpeaa)DE-He213 Stochastic partial differential equation (dpeaa)DE-He213 |
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misc Iterated stochastic integral misc Lévy area misc Stochastic simulation misc Julia misc Software toolbox misc Stochastic differential equation misc Stochastic partial differential equation |
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Elektronische Aufsätze Aufsätze Elektronische Ressource |
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An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox |
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An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox |
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Kastner, Felix |
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Numerical algorithms |
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Kastner, Felix Rößler, Andreas |
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analysis of approximation algorithms for iterated stochastic integrals and a julia and matlab simulation toolbox |
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An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox |
| abstract |
Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. © The Author(s) 2022 |
| abstractGer |
Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. © The Author(s) 2022 |
| abstract_unstemmed |
Abstract For the approximation and simulation of twofold iterated stochastic integrals and the corresponding Lévy areas w.r.t. a multi-dimensional Wiener process, we review four algorithms based on a Fourier series approach. Especially, the very efficient algorithm due to Wiktorsson and a newly proposed algorithm due to Mrongowius and Rößler are considered. To put recent advances into context, we analyse the four Fourier-based algorithms in a unified framework to highlight differences and similarities in their derivation. A comparison of theoretical properties is complemented by a numerical simulation that reveals the order of convergence for each algorithm. Further, concrete instructions for the choice of the optimal algorithm and parameters for the simulation of solutions for stochastic (partial) differential equations are given. Additionally, we provide advice for an efficient implementation of the considered algorithms and incorporated these insights into an open source toolbox that is freely available for both Julia and Matlab programming languages. The performance of this toolbox is analysed by comparing it to some existing implementations, where we observe a significant speed-up. © The Author(s) 2022 |
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1 |
| title_short |
An analysis of approximation algorithms for iterated stochastic integrals and a Julia and Matlab simulation toolbox |
| url |
https://dx.doi.org/10.1007/s11075-022-01401-z |
| remote_bool |
true |
| author2 |
Rößler, Andreas |
| author2Str |
Rößler, Andreas |
| ppnlink |
318468581 |
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c |
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| doi_str |
10.1007/s11075-022-01401-z |
| up_date |
2024-07-04T02:57:39.518Z |
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