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Maximum principle for optimal control problem of stochastic delay differential equations driven by fractional Brownian motions
Author(s) -
Wang Qiuxi,
Chen Feng,
Huang Fushan
Publication year - 2014
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2155
Subject(s) - stochastic differential equation , mathematics , brownian motion , fractional brownian motion , optimal control , quadratic equation , stochastic control , mathematical analysis , geometric brownian motion , differential equation , diffusion process , mathematical optimization , computer science , knowledge management , innovation diffusion , statistics , geometry
Summary In this paper, we consider the optimal control problem for delayed stochastic differential equations driven by fractional Brownian motions. Some necessary Pontryagin's type conditions are derived by considering the adjoint equations satisfying an anticipated backward stochastic differential equation driven by both fractional Brownian motions and the standard Brownian motions. Some new results on stochastic analysis about the control systems driven by fractional Brownian motions are presented. As an application, a linear quadratic problem is deduced, and a numerical example is shown to prove the effectiveness of our method. Copyright © 2014 John Wiley & Sons, Ltd.