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Discretisation of stochastic control problems for continuous time dynamics with delay

Authors
Journal
Journal of Computational and Applied Mathematics
0377-0427
Publisher
Elsevier
Publication Date
Volume
205
Issue
2
Identifiers
DOI: 10.1016/j.cam.2006.02.062
Keywords
  • Stochastic Delay Differential Equations
  • Stochastic Optimal Control
  • Finite-Difference Approximation

Abstract

Abstract 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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