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We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE).
Probability and related topics in physical sciences
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Propagation of chaos for a class of non-linear parabolic equations
H. P. Jr. McKean · 1967
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Multidimensional nonlinear diffusion arising in population genetics
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Asymptotic bounds for the expected L 1 L^{1} error of a multivariate kernel density estimator
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Processus associés à l’équation des milieux poreux
S. Benachour, P. Chassaing, B. Roynette, and P. Vallois · 1996
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Convergence rate for the approximation of the limit law of weakly interacting particles: application to the Burgers equation
M. Bossy and D. Talay · 1996
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Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models
S. Méléard · 1996
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Comparison of a stochastic particle method and a finite volume deterministic method applied to Burgers equation
M. Bossy, L. Fezoui, and S. Piperno · 1997
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Multidimensional diffusion processes
D. W. Stroock and S. R. S. Varadhan · 1997
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Propagation of chaos and fluctuations for a moderate model with smooth initial data
Probabilistic representation for solutions of an irregular porous media type equation: the irregular degenerate case
V. Barbu, M. Röckner, and F. Russo · 2011
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Counterparty risk valuation: A marked branching diffusion approach
P. Henry-Labordère · 2012
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Probabilistic and deterministic algorithms for space multidimensional irregular porous media equation
N. Belaribi, F. Cuvelier, and F. Russo · 2013
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A numerical algorithm for a class of BSDEs via the branching process
P. Henry-Labordère, X. Tan, and N. Touzi · 2014
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Stochastic differential equations, Backward SDEs, Partial differential equations
E. Pardoux and A. Raşcanu · 2014
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Fokker-Planck-Kolmogorov equations
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Backward stochastic differential equations and viscosity solutions of systems of semilinear parabolic and elliptic PDEs of second order
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Mathematical biology. I
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On the well-posedness of a class McKean Feynman-Kac equations
J. Lieber, N. Oudjane, and F. Russo
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V. I. Bogachev, N. V. Krylov, M. Röckner, and S. V. Shaposhnikov · 2015
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Branching diffusion representation of semilinear pdes and Monte Carlo approximations
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Probabilistic representation of a class of non-conservative nonlinear partial differential equations
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Monte-Carlo algorithms for a forward Feynman–Kac-type representation for semilinear nonconservative partial differential equations
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