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Infinite Horizon LQ Zero-Sum Stochastic Differential Games with Markovian Jumps
School of Management, Guangdong University of Technology, Guangzhou, China
School of Economics & Commence, Guangdong University of Technology, Guangzhou, China
School of Management, Guangdong University of Technology, Guangzhou, China
- 1 School of Management, Guangdong University of Technology, Guangzhou, China
- 2 School of Economics & Commence, Guangdong University of Technology, Guangzhou, China
- 3 School of Management, Guangdong University of Technology, Guangzhou, China
Applied Mathematics·Volume 03 (2012)·Pages 1321–1326·Published 31 October 2012·DOI10.4236/am.2012.330188
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Abstract
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.
KeywordsStochastic SystemsDifferential GamesMarkovian JumpsStochastic H<sub>∞</sub>Control
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