Geodesic
Diffusion approximation and optimal stochastic control
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 4, pp. 705-737

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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 $\delta$-optimal for the limit model remains $\delta$-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.
Keywords: stochastic control, stochastic differential equations, weak convergence, asymptotic optimality. 
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     author = {R. Liptser and W. J. Runggaldier and M. I. Taksar},
     title = {Diffusion approximation and optimal stochastic control},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {705--737},
     publisher = {mathdoc},
     volume = {44},
     number = {4},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_4_a0/}
}
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R. Liptser; W. J. Runggaldier; M. I. Taksar. Diffusion approximation and optimal stochastic control. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 4, pp. 705-737. http://geodesic.mathdoc.fr/item/TVP_1999_44_4_a0/