Title :
Numerical Solutions for Stochastic Differential Games With Regime Switching
Author :
Song, Qingshuo ; Yin, G. George ; Zhang, Zhimin
Author_Institution :
Dept. of Math., Univ. of Southern California, Los Angeles, CA
fDate :
3/1/2008 12:00:00 AM
Abstract :
This paper is concerned with numerical methods for stochastic differential games of regime-switching diffusions. Numerical methods using Markov chain approximation techniques are developed. A new proof of the existence of a saddle point for the stochastic differential game is provided. This new proof enables us to treat certain systems with nonseparable (in controls) structure. Convergence of the algorithms is derived by means of weak convergence methods. In addition, examples are also provided for demonstration purposes.
Keywords :
Markov processes; approximation theory; convergence of numerical methods; differential games; stochastic games; Markov chain approximation technique; numerical convergence method; numerical solutions; regime switching diffusion; stochastic differential game; Closed-form solution; Communication system traffic control; Constraint optimization; Control systems; Convergence of numerical methods; Mathematics; Stochastic processes; Stochastic systems; Systems engineering and theory; Traffic control; Controlled regime-switching diffusion; Markov chain approximation; convergence; saddle point; stochastic differential game;
Journal_Title :
Automatic Control, IEEE Transactions on
DOI :
10.1109/TAC.2007.915169
