Some moment inequalities for fuzzy martingales and their applications
Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and...
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| Autor*in: |
Ahmadzade, Hamed [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Anmerkung: |
© Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( |
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| Übergeordnetes Werk: |
Enthalten in: Journal of Uncertainty Analysis and Applications - Berlin : SpringerOpen, 2013, 2(2014), 1 vom: 31. März |
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volume:2 ; year:2014 ; number:1 ; day:31 ; month:03 |
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10.1186/2195-5468-2-7 |
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| 520 | |a Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. | ||
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| 700 | 1 | |a Bozorgnia, Abolghasem |4 aut | |
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10.1186/2195-5468-2-7 doi (DE-627)SPR036488127 (SPR)2195-5468-2-7-e DE-627 ger DE-627 rakwb eng Ahmadzade, Hamed verfasserin aut Some moment inequalities for fuzzy martingales and their applications 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. Fuzzy random variable (dpeaa)DE-He213 Fuzzy martingale (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Strong convergence (dpeaa)DE-He213 Amini, Mohammad aut Taheri, Seyed Mahmoud aut Bozorgnia, Abolghasem aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 2(2014), 1 vom: 31. März (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:2 year:2014 number:1 day:31 month:03 https://dx.doi.org/10.1186/2195-5468-2-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2014 1 31 03 |
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10.1186/2195-5468-2-7 doi (DE-627)SPR036488127 (SPR)2195-5468-2-7-e DE-627 ger DE-627 rakwb eng Ahmadzade, Hamed verfasserin aut Some moment inequalities for fuzzy martingales and their applications 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. Fuzzy random variable (dpeaa)DE-He213 Fuzzy martingale (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Strong convergence (dpeaa)DE-He213 Amini, Mohammad aut Taheri, Seyed Mahmoud aut Bozorgnia, Abolghasem aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 2(2014), 1 vom: 31. März (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:2 year:2014 number:1 day:31 month:03 https://dx.doi.org/10.1186/2195-5468-2-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2014 1 31 03 |
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10.1186/2195-5468-2-7 doi (DE-627)SPR036488127 (SPR)2195-5468-2-7-e DE-627 ger DE-627 rakwb eng Ahmadzade, Hamed verfasserin aut Some moment inequalities for fuzzy martingales and their applications 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. Fuzzy random variable (dpeaa)DE-He213 Fuzzy martingale (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Strong convergence (dpeaa)DE-He213 Amini, Mohammad aut Taheri, Seyed Mahmoud aut Bozorgnia, Abolghasem aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 2(2014), 1 vom: 31. März (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:2 year:2014 number:1 day:31 month:03 https://dx.doi.org/10.1186/2195-5468-2-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2014 1 31 03 |
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10.1186/2195-5468-2-7 doi (DE-627)SPR036488127 (SPR)2195-5468-2-7-e DE-627 ger DE-627 rakwb eng Ahmadzade, Hamed verfasserin aut Some moment inequalities for fuzzy martingales and their applications 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. Fuzzy random variable (dpeaa)DE-He213 Fuzzy martingale (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Strong convergence (dpeaa)DE-He213 Amini, Mohammad aut Taheri, Seyed Mahmoud aut Bozorgnia, Abolghasem aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 2(2014), 1 vom: 31. März (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:2 year:2014 number:1 day:31 month:03 https://dx.doi.org/10.1186/2195-5468-2-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2014 1 31 03 |
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10.1186/2195-5468-2-7 doi (DE-627)SPR036488127 (SPR)2195-5468-2-7-e DE-627 ger DE-627 rakwb eng Ahmadzade, Hamed verfasserin aut Some moment inequalities for fuzzy martingales and their applications 2014 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. Fuzzy random variable (dpeaa)DE-He213 Fuzzy martingale (dpeaa)DE-He213 Weak convergence (dpeaa)DE-He213 Strong convergence (dpeaa)DE-He213 Amini, Mohammad aut Taheri, Seyed Mahmoud aut Bozorgnia, Abolghasem aut Enthalten in Journal of Uncertainty Analysis and Applications Berlin : SpringerOpen, 2013 2(2014), 1 vom: 31. März (DE-627)745007392 (DE-600)2713511-1 2195-5468 nnns volume:2 year:2014 number:1 day:31 month:03 https://dx.doi.org/10.1186/2195-5468-2-7 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2014 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 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_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2 2014 1 31 03 |
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Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( |
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Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( |
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Abstract Martingales are a class of stochastic processes which has had profound influence on the development of probability theory and stochastic processes. Some recent developments are related to mathematical finance. In the real world, some information about these phenomena might be imprecise and represented in the form of vague quantities. In these situations, we need to generalize classical methods to vague environment. Thus, fuzzy martingales have been extended as a vague perception of real-valued martingales. In this paper, some moment inequalities are presented for fuzzy martingales. Several convergence theorems are established based on these inequalities. As an application of convergence theorems, a weak law of large numbers for fuzzy martingales is stated. Furthermore, a few examples are devoted to clarify the main results. © Ahmadzade et al.; licensee Springer. 2014. This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( |
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