This article is cited in 7 scientific papers (total in 7 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
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.
linear stochastic differential equation, almost sure convergence of stochastic processes, linear regulator, stochastic optimality, discounting, asymptotic solution method.
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Computational Mathematics and Mathematical Physics, 2014, 54:1, 83–96
E. S. Palamarchuk, “Asymptotic behavior of the solution to a linear stochastic differential equation and almost sure optimality for a controlled stochastic process”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 89–103; Comput. Math. Math. Phys., 54:1 (2014), 83–96
Citation in format AMSBIB
\paper Asymptotic behavior of the solution to a linear stochastic differential equation and almost sure optimality for a controlled stochastic process
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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