Stability of Stochastic Functional Differential Equations with Regime-Switching: Analysis Using Dupire’s Functional Itô Formula
Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. Novel conditions for stability, which are different from those in the existing literature,...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Nguyen, Dang Hai [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Nature B.V. 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Potential analysis - Springer Netherlands, 1992, 53(2019), 1 vom: 22. Feb., Seite 247-265 |
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| Übergeordnetes Werk: |
volume:53 ; year:2019 ; number:1 ; day:22 ; month:02 ; pages:247-265 |
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| DOI / URN: |
10.1007/s11118-019-09767-x |
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OLC2046685830 |
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| 520 | |a Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. Novel conditions for stability, which are different from those in the existing literature, are given in terms of Lyapunov functionals. It is demonstrated that the conditions are useful for stochastic stabilization. It is also shown that adding a diffusion term can stabilize an unstable system of deterministic differential equations with Markov switching. Furthermore, a robustness result is obtained, which states that the stability of stochastic differential equations with regime-switching is preserved under delayed perturbations when the delay is small enough. | ||
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10.1007/s11118-019-09767-x doi (DE-627)OLC2046685830 (DE-He213)s11118-019-09767-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Nguyen, Dang Hai verfasserin aut Stability of Stochastic Functional Differential Equations with Regime-Switching: Analysis Using Dupire’s Functional Itô Formula 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. Novel conditions for stability, which are different from those in the existing literature, are given in terms of Lyapunov functionals. It is demonstrated that the conditions are useful for stochastic stabilization. It is also shown that adding a diffusion term can stabilize an unstable system of deterministic differential equations with Markov switching. Furthermore, a robustness result is obtained, which states that the stability of stochastic differential equations with regime-switching is preserved under delayed perturbations when the delay is small enough. Switching diffusion Functional stochastic differential equation with switching Stability Yin, George aut Enthalten in Potential analysis Springer Netherlands, 1992 53(2019), 1 vom: 22. Feb., Seite 247-265 (DE-627)165647787 (DE-600)33485-6 (DE-576)032989911 0926-2601 nnns volume:53 year:2019 number:1 day:22 month:02 pages:247-265 https://doi.org/10.1007/s11118-019-09767-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 53 2019 1 22 02 247-265 |
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10.1007/s11118-019-09767-x doi (DE-627)OLC2046685830 (DE-He213)s11118-019-09767-x-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Nguyen, Dang Hai verfasserin aut Stability of Stochastic Functional Differential Equations with Regime-Switching: Analysis Using Dupire’s Functional Itô Formula 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. Novel conditions for stability, which are different from those in the existing literature, are given in terms of Lyapunov functionals. It is demonstrated that the conditions are useful for stochastic stabilization. It is also shown that adding a diffusion term can stabilize an unstable system of deterministic differential equations with Markov switching. Furthermore, a robustness result is obtained, which states that the stability of stochastic differential equations with regime-switching is preserved under delayed perturbations when the delay is small enough. Switching diffusion Functional stochastic differential equation with switching Stability Yin, George aut Enthalten in Potential analysis Springer Netherlands, 1992 53(2019), 1 vom: 22. Feb., Seite 247-265 (DE-627)165647787 (DE-600)33485-6 (DE-576)032989911 0926-2601 nnns volume:53 year:2019 number:1 day:22 month:02 pages:247-265 https://doi.org/10.1007/s11118-019-09767-x lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 AR 53 2019 1 22 02 247-265 |
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Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. Novel conditions for stability, which are different from those in the existing literature, are given in terms of Lyapunov functionals. It is demonstrated that the conditions are useful for stochastic stabilization. It is also shown that adding a diffusion term can stabilize an unstable system of deterministic differential equations with Markov switching. Furthermore, a robustness result is obtained, which states that the stability of stochastic differential equations with regime-switching is preserved under delayed perturbations when the delay is small enough. © Springer Nature B.V. 2019 |
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Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. Novel conditions for stability, which are different from those in the existing literature, are given in terms of Lyapunov functionals. It is demonstrated that the conditions are useful for stochastic stabilization. It is also shown that adding a diffusion term can stabilize an unstable system of deterministic differential equations with Markov switching. Furthermore, a robustness result is obtained, which states that the stability of stochastic differential equations with regime-switching is preserved under delayed perturbations when the delay is small enough. © Springer Nature B.V. 2019 |
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Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. Novel conditions for stability, which are different from those in the existing literature, are given in terms of Lyapunov functionals. It is demonstrated that the conditions are useful for stochastic stabilization. It is also shown that adding a diffusion term can stabilize an unstable system of deterministic differential equations with Markov switching. Furthermore, a robustness result is obtained, which states that the stability of stochastic differential equations with regime-switching is preserved under delayed perturbations when the delay is small enough. © Springer Nature B.V. 2019 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2046685830</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230504154330.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2019 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s11118-019-09767-x</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2046685830</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s11118-019-09767-x-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">510</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">17,1</subfield><subfield code="2">ssgn</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Nguyen, Dang Hai</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stability of Stochastic Functional Differential Equations with Regime-Switching: Analysis Using Dupire’s Functional Itô Formula</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Nature B.V. 2019</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This work focuses on almost sure and Lp stability of stochastic functional differential equations by using Lyapunov functionals with the help of the recently developed Dupire’s functional Itô formula. 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