Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps


This paper studies a class of continuous-time two person zero-sum stochastic differential games characterized by linear It?’s differential equation with state-dependent noise and Markovian parameter jumps. Under the assumption of stochastic stabilizability, necessary and sufficient condition for the existence of the optimal control strategies is presented by means of a system of coupled algebraic Riccati equations via using the stochastic optimal control theory. Furthermore, the stochastic H control problem for stochastic systems with Markovian jumps is discussed as an immediate application, and meanwhile, an illustrative example is presented.

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H. Zhu, C. Zhang and N. Bin, "Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps," Applied Mathematics, Vol. 3 No. 10A, 2012, pp. 1321-1326. doi: 10.4236/am.2012.330188.

Conflicts of Interest

The authors declare no conflicts of interest.


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