This article is cited in 16 papers

Asymptotic behavior of the solution to a linear stochastic differential equation and almost sure optimality for a controlled stochastic process

E. S. Palamarchuk

Central Economics and Mathematics Institute, Russian Academy of Sciences, Nakhimovskii pr. 47, Moscow, 117418, Russia

Abstract: The asymptotic behavior of a stochastic process satisfying a linear stochastic differential equation is analyzed. More specifically, the problem is solved of finding a normalizing function such that the normalized process tends to zero with probability 1. The explicit expression found for the function involves the parameters of the perturbing process, and the function itself has a simple interpretation. The solution of the indicated problem makes it possible to considerably improve almost sure optimality results for a stochastic linear regulator on an infinite time interval.

Key words: linear stochastic differential equation, almost sure convergence of stochastic processes, linear regulator, stochastic optimality, discounting, asymptotic solution method.

UDC: 519.63

Received: 13.03.2013

DOI: 10.7868/S0044466914010128

 English version: Computational Mathematics and Mathematical Physics, 2014, 54:1, 83–96

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