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Zap. Nauchn. Sem. POMI, 2015, Volume 437, Pages 184–206 (Mi znsl6178)  

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00237
15-31-20082
Partially supported by the RFBR grants 14-01-00237 and 15-31-20082.


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English version:
Journal of Mathematical Sciences (New York), 2016, 216:1, 120–135

Bibliographic databases:

UDC: 517.956.4+519.216.2
Received: 20.09.2015
Language:

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

Citation in format AMSBIB
\Bibitem{Man15}
\by O.~A.~Manita
\paper Nonlinear Fokker--Planck--Kolmogorov equations in Hilbert spaces
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XXVI. Representation theory, dynamical systems, combinatorial methods
\serial Zap. Nauchn. Sem. POMI
\yr 2015
\vol 437
\pages 184--206
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6178}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3499913}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2016
\vol 216
\issue 1
\pages 120--135
\crossref{https://doi.org/10.1007/s10958-016-2891-1}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84969821515}


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