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The existence and uniqueness of measure-valued solutions to stochastic nonlinear, non-local Fokker-Planck equations is proven.
A class of Markov processes associated with nonlinear parabolic equations
H. P. McKean, Jr · 1966
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Propagation of chaos for a class of non-linear parabolic equations
H. P. McKean, Jr · 1967
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Uniqueness and nonuniqueness of solutions of Vlasov-McKean equations
M. Scheutzow · 1987
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Topics in propagation of chaos
A.-S. Sznitman · 1991
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A duality analysis on stochastic partial differential equations
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Stochastic McKean-Vlasov equations
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Particle representations for a class of nonlinear spdes
T. G. Kurtz and J. Xiong · 1999
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Numerical solutions for a class of SPDEs with application to filtering
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On semi-linear degenerate backward stochastic partial differential equations
Y. Hu, J. Ma, and J. Yong · 2002
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Semi-linear systems of backward stochastic partial differential equations in ℝ n \mathbb{R}^{n}
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Large deviation principle for a stochastic Navier-Stokes equation in its vorticity form for a two-dimensional incompressible flow
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Jeux à champ moyen. I. Le cas stationnaire
J.-M. Lasry and P.-L. Lions · 2006
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Jeux à champ moyen. II. Horizon fini et contrôle optimal
J.-M. Lasry and P.-L. Lions · 2006
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Measure theory
V. I. Bogachev · 2007
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Measure theory. Vol. I, II
V. I. Bogachev · 2007
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Mean field games
J.-M. Lasry and P.-L. Lions · 2007
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Parabolic equations for measures on infinite-dimensional spaces
V. I. Bogachev, D. Da Prato, and M. Röckner · 2008
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Elliptic and parabolic equations for measures
V. I. Bogachev, N. V. Krylov, and M. Röckner · 2009
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Stochastic flows and signed measure valued stochastic partial differential equations
P. M. Kotelenez · 2010
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On the Hahn-Jordan decomposition for signed measure valued stochastic partial differential equations
P. M. Kotelenez and B. T. Seadler · 2012
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Stochastic partial differential equations: an introduction
W. Liu and M. Röckner · 2015
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On uniqueness of solutions to nonlinear Fokker-Planck-Kolmogorov equations
O. A. Manita, M. S. Romanov, and S. V. Shaposhnikov · 2015
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Propagation of chaos for interacting particles subject to environmental noise
M. Coghi and F. Flandoli · 2016
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Stochastic scalar conservation laws driven by rough paths
P. K. Friz and B. Gess · 2016
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Regularization by noise for stochastic hamilton–jacobi equations
P. Gassiat and B. Gess · 2016
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Stochastic partial differential equations: a rough paths view on weak solutions via Feynman-Kac
J. Diehl, P. K. Friz, and W. Stannat · 2017
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Well-posedness of stochastic porous media equations with nonlinear, conservative noise
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