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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 1, Pages 14–25 (Mi timm1255)  
Estimation of the evolution of a random set

B. I. Anan'evab

a Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
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Abstract: An estimation problem for a random set that is a reachability domain of the Ito differential equation with respect to its initial data is considered. The Markov property of the reachability set in the space of closed sets is proved. For the purposes of numerical solution, a random initial set of the differential equation is approximated by a finite set on an integer multidimensional grid, and the differential equation is replaced by a multistep Markov chain. Examples are considered.
Keywords: stochastic differential equation, Markov chain, random set.
Received: 25.09.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 296, Issue 1, Pages 31–42
DOI: https://doi.org/10.1134/S0081543817020043
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: B. I. Anan'ev, “Estimation of the evolution of a random set”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 1, 2016, 14–25; Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 31–42
Citation in format AMSBIB
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