Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System

Hong Zhang; Jingyi Wang; Tengyu Zhao; Li Zhou

doi:doi:10.11648/j.pamj.20150403.17

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Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System

Hong Zhang, Jingyi Wang, Tengyu Zhao, Li Zhou

Published in Pure and Applied Mathematics Journal (Volume 4, Issue 3)

Received: 22 April 2015 Accepted: 5 May 2015 Published: 1 June 2015

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Abstract

Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.

Published in	Pure and Applied Mathematics Journal (Volume 4, Issue 3)
DOI	10.11648/j.pamj.20150403.17
Page(s)	101-108
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Mean-Field Backward Doubly, Stochastic System, Stochastic Control

References

[1]	A. Szukala, A Knese-type theorem for euqation x=f (t, x) in locally convex spaces, Journal for analysis and its applications, 18 (1999), 1101-1106.
[2]	M. Tang and Q. Zhang, Optimal variational principle for backward stochastic control systems associated with Levy processes, Sci China Math, 55 (2012), 745-761.
[3]	SevaS. Tang and X. Li, Necessary condition for optimal control of stochastic systems with random jumps, SIAM J Control Optim, 32 (1994), 1447-1475.
[4]	J. Valero, On the kneser property for some parapolic problems, Topology and its applicanons, 155 (2005), 975-989.
[5]	Z. Wu, Maximum principle for optimal control problem of fully coupled forward-backward stochastic systems, J. Systems Sci. Math. Sci., 11 (1998), 249-259.
[6]	Z. Wu, Forward-backward stochastic differential equations with Brownian Motion and Process Poisson, Acta Math. Appl. Sinica, English Series, 15 (1999), 433-443.
[7]	Z. Wu, A maximum principle for partially observed optimal control of forward-backward stochastic control systems, Sci China Ser F, 53 (2010), 2205-2214.
[8]	Z. Wu and Z. Yu, Fully coupled forward-backward stochastic differential equations and related partial differential equations system, Chinese Ann Math Ser A, 25 (2004), 457-468
[9]	H. Xiao and G. Wang, A necessary condition for optimal control of initial coupled forward-backward stochastic differential equations with partial information, J. Appl. Math. Comput., 37 (2011), 347-359.
[10]	J. Xiong, An Introduction to Stochastic Filtering Theory, London, U.K.: Oxford University Press, 2008.

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APA Style

Hong Zhang, Jingyi Wang, Tengyu Zhao, Li Zhou. (2015). Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System. Pure and Applied Mathematics Journal, 4(3), 101-108. https://doi.org/10.11648/j.pamj.20150403.17

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ACS Style

Hong Zhang; Jingyi Wang; Tengyu Zhao; Li Zhou. Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System. Pure Appl. Math. J. 2015, 4(3), 101-108. doi: 10.11648/j.pamj.20150403.17

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AMA Style

Hong Zhang, Jingyi Wang, Tengyu Zhao, Li Zhou. Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System. Pure Appl Math J. 2015;4(3):101-108. doi: 10.11648/j.pamj.20150403.17

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@article{10.11648/j.pamj.20150403.17,
  author = {Hong Zhang and Jingyi Wang and Tengyu Zhao and Li Zhou},
  title = {Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {101-108},
  doi = {10.11648/j.pamj.20150403.17},
  url = {https://doi.org/10.11648/j.pamj.20150403.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.17},
  abstract = {Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.},
 year = {2015}
}

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TY  - JOUR
T1  - Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System
AU  - Hong Zhang
AU  - Jingyi Wang
AU  - Tengyu Zhao
AU  - Li Zhou
Y1  - 2015/06/01
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.17
DO  - 10.11648/j.pamj.20150403.17
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 101
EP  - 108
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.17
AB  - Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.
VL  - 4
IS  - 3
ER  -

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Author Information

Hong Zhang

School of Information, Beijing Wuzi University, Beijing, China
Jingyi Wang

School of Banking and Finance, University of International Business and Economics, Beijing, China
Tengyu Zhao

School of Management Science and Engineering, Central University of Finance and Economics, Beijing, China
Li Zhou

School of Information, Beijing Wuzi University, Beijing, China

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Plain Text BibTeX RIS

APA Style

Hong Zhang, Jingyi Wang, Tengyu Zhao, Li Zhou. (2015). Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System. Pure and Applied Mathematics Journal, 4(3), 101-108. https://doi.org/10.11648/j.pamj.20150403.17

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ACS Style

Hong Zhang; Jingyi Wang; Tengyu Zhao; Li Zhou. Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System. Pure Appl. Math. J. 2015, 4(3), 101-108. doi: 10.11648/j.pamj.20150403.17

Copy | Download

AMA Style

Hong Zhang, Jingyi Wang, Tengyu Zhao, Li Zhou. Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System. Pure Appl Math J. 2015;4(3):101-108. doi: 10.11648/j.pamj.20150403.17

Copy | Download

@article{10.11648/j.pamj.20150403.17,
  author = {Hong Zhang and Jingyi Wang and Tengyu Zhao and Li Zhou},
  title = {Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {4},
  number = {3},
  pages = {101-108},
  doi = {10.11648/j.pamj.20150403.17},
  url = {https://doi.org/10.11648/j.pamj.20150403.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20150403.17},
  abstract = {Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Maximum Principle and the Applications of Mean-Field Backward Doubly Stochastic System
AU  - Hong Zhang
AU  - Jingyi Wang
AU  - Tengyu Zhao
AU  - Li Zhou
Y1  - 2015/06/01
PY  - 2015
N1  - https://doi.org/10.11648/j.pamj.20150403.17
DO  - 10.11648/j.pamj.20150403.17
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 101
EP  - 108
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20150403.17
AB  - Since Pardoux and Peng firstly studied the following nonlinear backward stochastic differential equations in 1990. The theory of BSDE has been widely studied and applied, especially in the stochastic control, stochastic differential games, financial mathematics and partial differential equations. In 1994, Pardoux and Peng came up with backward doubly stochastic differential equations to give the probabilistic interpretation for stochastic partial differential equations. Backward doubly stochastic differential equations theory has been widely studied because of its importance in stochastic partial differential equations and stochastic control problems. In this article, we will study the theory of doubly stochastic systems and related topics further.
VL  - 4
IS  - 3
ER  -

Copy | Download