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Zapiski Nauchnykh Seminarov POMI, 2015, Volume 437, Pages 184–206
(Mi znsl6178)
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This article is cited in 3 scientific papers (total in 3 papers)
Nonlinear Fokker–Planck–Kolmogorov equations in Hilbert spaces
O. A. Manita Department of Mechanics and Mathematics, Moscow State University, Moscow, Russia
Abstract:
We study the Cauchy problem for nonlinear Fokker–Planck–Kolmogorov equations for probability measures on a Hilbert space, corresponding to stochastic partial differential equations. Sufficient conditions for the uniqueness of probability solutions for a cylindrical diffusion operator and for a possibly degenerate diffusion operator are given. A new general existence result is established without explicit growth restrictions on the coefficients.
Key words and phrases:
nonlinear Fokker–Planck–Kolmogorov equation, Cauchy problem, SPDE, uniqueness of solutions, transition probability.
Received: 20.09.2015
Citation:
O. A. Manita, “Nonlinear Fokker–Planck–Kolmogorov equations in Hilbert spaces”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Zap. Nauchn. Sem. POMI, 437, POMI, St. Petersburg, 2015, 184–206; J. Math. Sci. (N. Y.), 216:1 (2016), 120–135
Linking options:
https://www.mathnet.ru/eng/znsl6178 https://www.mathnet.ru/eng/znsl/v437/p184
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Abstract page: | 195 | Full-text PDF : | 60 | References: | 33 |
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