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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
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
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
Linking options:
https://www.mathnet.ru/eng/zvmmf10991 https://www.mathnet.ru/eng/zvmmf/v60/i10/p1741
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