Approximation of Stochastic Differential Equations with Modified Fractional Brownian Motion

被引：0

作者：

Grecksch, W. ^{[1
]}

Ahn, V. V. ^{[2
]}

机构：

[1] Univ Halle Wittenberg, Fachbereich Math & Informat, Inst Optimierung & Stochast, D-06099 Halle, Saale, Germany

[2] Queensland Univ Technol, Ctr Stat Sci & Ind Math, Brisbane, Qld 4001, Australia

来源：

ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN | 1998年 / 17卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

Modified fractional Brownian motion; splitting method; stochastic integral; epsilon-optimal control;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The modified fractional Brownian motion is a special semimartingale. This stochastic process is suitable for studying the phenomenon of long-range dependence in a wide range of fields. This paper introduces stochastic differential equations with respect to modified fractional Brownian motion. The solution of these equations is approximated by a splitting method whose convergence in probability is proved. An application of this method to determine epsilon-optimal controls for a stochastic control problem is also given.

引用

页码：715 / 727

页数：13

共 50 条

[1] Approximation of stochastic differential equations driven by fractional Brownian motion
Lisei, Hannelore
Soos, Anna
[J]. SEMINAR ON STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS V, 2008, 59 : 227 - 241
[2] Modified Euler approximation of stochastic differential equation driven by Brownian motion and fractional Brownian motion
Liu, Weiguo
Luo, Jiaowan
[J]. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2017, 46 (15) : 7427 - 7443
[3] Optimal pointwise approximation of stochastic differential equations driven by fractional Brownian motion
Neuenkirch, Andreas
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2008, 118 (12) : 2294 - 2333
[4] Approximation of solutions of stochastic differential equations with fractional Brownian motion by solutions of random ordinary differential equations
Ral'chenko K.V.
Shevchenko H.M.
[J]. Ukrainian Mathematical Journal, 2011, 62 (9) : 1460 - 1475
[5] APPROXIMATION OF SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS WITH FRACTIONAL BROWNIAN MOTION BY SOLUTIONS OF RANDOM ORDINARY DIFFERENTIAL EQUATIONS
Ral'chenko, K. V.
Shevchenko, H. M.
[J]. UKRAINIAN MATHEMATICAL JOURNAL, 2011, 62 (09) : 1460 - 1475
[6] Stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Guerra, Joao
Nualart, David
[J]. STOCHASTIC ANALYSIS AND APPLICATIONS, 2008, 26 (05) : 1053 - 1075
[7] Stochastic differential equations driven by fractional Brownian motion
Xu, Liping
Luo, Jiaowan
[J]. STATISTICS & PROBABILITY LETTERS, 2018, 142 : 102 - 108
[8] Stochastic averaging for stochastic differential equations driven by fractional Brownian motion and standard Brownian motion
Pei, Bin
Xu, Yong
Wu, Jiang-Lun
[J]. APPLIED MATHEMATICS LETTERS, 2020, 100
[9] Impulsive stochastic fractional differential equations driven by fractional Brownian motion
Abouagwa, Mahmoud
Cheng, Feifei
Li, Ji
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[10] Nonlocal fractional stochastic differential equations driven by fractional Brownian motion
Lv, Jingyun
Yang, Xiaoyuan
[J]. ADVANCES IN DIFFERENCE EQUATIONS, 2017,

← 1 2 3 4 5 →