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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 1, Pages 89–103
DOI: https://doi.org/10.7868/S0044466914010128 (Mi zvmmf9975) 		 
This article is cited in 15 scientific papers (total in 15 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
Full-text PDF (472 kB) Citations (15)
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DOI: https://doi.org/10.7868/S0044466914010128
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.
Received: 13.03.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 1, Pages 83–96
DOI: https://doi.org/10.1134/S0965542514010114
Bibliographic databases:
Document Type: Article
UDC: 519.63
Language: Russian
Citation: 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
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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