On Uniqueness of a Probability Solution to the Cauchy Problem for the Fokker–Planck–Kolmogorov Equation

DOI10.1137/S0040585X97985212zbMath1238.35168OpenAlexW2077642468MaRDI QIDQ2882764

Stanislav V. Shaposhnikov

Publication date: 7 May 2012

Published in: Theory of Probability & Its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s0040585x97985212

zbMATH Keywords

transition probabilitiesFokker-Planck-Kolmogorov equationuniqueness of the Cauchy problem for a parabolic equation

Mathematics Subject Classification ID

Initial value problems for second-order parabolic equations (35K15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Fokker-Planck equations (35Q84) PDEs with measure (35R06)

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Nonlinear parabolic equations for measures ⋮ On the Cauchy problem for Fokker-Planck-Kolmogorov equations with potential terms on arbitrary domains ⋮ Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations ⋮ On uniqueness of solutions to the Cauchy problem for degenerate Fokker-Planck-Kolmogorov equations ⋮ On the Ambrosio-Figalli-Trevisan superposition principle for probability solutions to Fokker-Planck-Kolmogorov equations ⋮ On the superposition principle for Fokker-Planck-Kolmogorov equations ⋮ Uniqueness problems for degenerate Fokker-Planck-Kolmogorov equations ⋮ On uniqueness of probability solutions of the Fokker-Planck-Kolmogorov equation ⋮ Unnamed Item ⋮ Convergence to Periodic Probability Solutions in Fokker--Planck Equations ⋮ Convergence to equilibrium in Fokker-Planck equations ⋮ Neural ODEs as the deep limit of ResNets with constant weights

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