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November  2015, 35(11): 5435-5445. doi: 10.3934/dcds.2015.35.5435

## Some linear-quadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions

 1 Department of Mathematics, University of Kansas, Lawrence, KS 66045, United States

Received  December 2012 Revised  February 2014 Published  May 2015

A noncooperative, two person, zero sum, stochastic differential game is formulated and solved that is described by a linear stochastic equation in a Hilbert space with a fractional Brownian motion and a quadratic payoff functional for the two players. The stochastic equation can model stochastic partial differential equations not only with distributed strategies and noise but also with control strategies and noise restricted to the boundary of the domain. The optimal strategies for the two players are given explicitly. The verification method is a generalization of completion of squares and provides the optimal strategies directly without solving partial differential equations or backward stochastic differential equations. Some examples of games described by stochastic partial differential equations are given.
Citation: Tyrone E. Duncan. Some linear-quadratic stochastic differential games for equations in Hilbert spaces with fractional Brownian motions. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5435-5445. doi: 10.3934/dcds.2015.35.5435
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