Diffusion approximation and optimal stochastic control

R. Liptser, W. J. Runggaldier, M. Taksar

Research output: Contribution to journalArticlepeer-review


In this paper a stochastic control model is studied that admits a diffusion approximation. In the prelimit model the disturbances are given by noise processes of various types: additive stationary noise, rapidly oscillating processes, and discontinuous processes with large intensity for jumps of small size. We show that a feedback control that satisfies a Lipschitz condition and is δ-optimal for the limit model remains δ-optimal also in the prelimit model. The method of proof uses the technique of weak convergence of stochastic processes. The result that is obtained extends a previous work by the authors, where the limit model is deterministic.

Original languageEnglish
Pages (from-to)669-696
Number of pages28
JournalTheory of Probability and its Applications
Issue number4
StatePublished - Dec 1999


  • Asymptotic optimality
  • Stochastic control
  • Stochastic differential equations
  • Weak convergence


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