Discretisation of stochastic control problems for continuous time dynamics with delay

Details Discretisation of stochastic control problems for continuous time dynamics with delay Discretisation of stochastic control problems for continuous time dynamics with delay

2006-02-17

arxiv.org/abs/math/0602385v1

Mathematics

Optimization and Control

submitted to JCAM

Scientific paper

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.

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