Linear Stochastic Differential Games with State Dependent Fractional Brownian Motion

被引：0
|
作者：
Duncan, T. E. [1 ]
Pasik-Duncan, B. [1 ]
机构：
[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA
来源：
IFAC PAPERSONLINE | 2017年 / 50卷 / 01期
关键词：
linear stochastic differential games; stochastic games with state dependent noise; fractional Brownian motions; explicit control strategies; Nash equilibria;
D O I：
10.1016/j.ifacol.2017.08.295
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
A two person, zero-sum, noncooperative stochastic differential game is formulated and solved for a multidimensional linear stochastic system that has a quadratic payoff and a linear state dependent scalar fractional Brownian motion noise process in the stochastic system. The strategies are restricted to be linear feedback. A Riccati equation is given that provides the optimal control strategies for the two players using a direct method and this Riccati equation is different from the one for the corresponding problem with an additive Brownian motion. The strategies are shown to form a Nash equilibrium. The method presented and applied here for the solution requires only some elementary notions from a stochastic calculus for a fractional Brownian motion. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.
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页码：1484 / 1488
页数：5
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