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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2020, Volume 60, Number 10, Pages 1741–1756
DOI: https://doi.org/10.31857/S0044466920100154
(Mi zvmmf10991)
 

This article is cited in 8 scientific papers (total in 8 papers)

Partial Differential Equations

Stochastic processes on the group of orthogonal matrices and evolution equations describing them

K. Yu. Zamanaa, V. Zh. Sakbaevabcd, O. G. Smolyanovae

a Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, 141701 Russia
b Institute of Information Technologies, Mathematics, and Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950 Russia
c Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, 119991 Russia
d Institute of Mathematics with Computing Center, Ufa Federal Research Center, Russian Academy of Sciences, Ufa, 450008 Bashkortostan, Russia
e Lomonosov Moscow State University
Citations (8)
References:
Abstract: Stochastic processes that take values in the group of orthogonal transformations of a finite-dimensional Euclidean space and are noncommutative analogues of processes with independent increments are considered. Such processes are defined as limits of noncommutative analogues of random walks in the group of orthogonal transformations. These random walks are compositions of independent random orthogonal transformations of Euclidean space. In particular, noncommutative analogues of diffusion processes with values in the group of orthogonal transformations are defined in this manner. Kolmogorov backward equations are derived for these processes.
Key words: random linear operator, random operator-valued function, operator-valued stochastic process, law of large numbers, Kolmogorov equation.
Received: 07.02.2020
Revised: 20.02.2020
Accepted: 09.06.2020
English version:
Computational Mathematics and Mathematical Physics, 2020, Volume 60, Issue 10, Pages 1686–1700
DOI: https://doi.org/10.1134/S0965542520100140
Bibliographic databases:
Document Type: Article
UDC: 517.63
Language: Russian
Citation: K. Yu. Zamana, V. Zh. Sakbaev, O. G. Smolyanov, “Stochastic processes on the group of orthogonal matrices and evolution equations describing them”, Zh. Vychisl. Mat. Mat. Fiz., 60:10 (2020), 1741–1756; Comput. Math. Math. Phys., 60:10 (2020), 1686–1700
Citation in format AMSBIB
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  • This publication is cited in the following 8 articles:
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