Numerical methods for stochastic control problems in continuous time
Numerical methods for stochastic control problems in continuous time
Introduction to the numerical analysis of stochastic delay differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
Representation and Control of Infinite Dimensional Systems (Systems & Control: Foundations & Applications)
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As a main step in the numerical solution of control problems in continuous time, the controlled process is approximated by sequences of controlled Markov chains, thus discretising time and space. A new feature in this context is to allow for delay in the dynamics. The existence of an optimal strategy with respect to the cost functional can be guaranteed in the class of relaxed controls. Weak convergence of the approximating extended Markov chains to the original process together with convergence of the associated optimal strategies is established.