Some Linear-Quadratic Stochastic Differential Games Driven by State Dependent Gauss-Volterra Processes

2019 ◽  
pp. 173-179
Author(s):  
Tyrone E. Duncan ◽  
Bozenna Pasik-Duncan
Keyword(s):  
Differential Games ◽  
Stochastic Differential Games ◽  
Linear Quadratic ◽  
State Dependent

scholarly journals Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Huiying Sun ◽  
Meng Li ◽  
Shenglin Ji ◽  
Long Yan
Keyword(s):  
Linear Systems ◽  
Differential Games ◽  
Discrete Time ◽  
Infinite Horizon ◽  
Stochastic Differential Games ◽  
Markovian Jump ◽  
Linear Quadratic ◽  
Jump Linear Systems ◽  
State Dependent ◽  
Markovian Jump Linear Systems

We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ) differential games. A necessary and sufficient condition involved with the connection between stochasticTn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochasticTn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs). Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

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