Related papers: Feynman-Kac formula under a finite entropy conditi…

We prove Feynman-Kac formulas for solutions to elliptic and parabolic boundary value and obstacle problems associated with a general Markov diffusion process. Our diffusion model covers several popular stochastic volatility models, such as…

We prove the existence of a $B$-continuous viscosity solution for a class of infinite dimensional semilinear partial differential equations (PDEs) using probabilistic methods. Our approach also yields a stochastic representation formula for…

It is known that Markovian forward-backward stochastic differential equations provide nonlinear Feynman-Kac representation formulae for semilinear parabolic PDEs. We show that non-Markovian forward-backward stochastic differential equations…

We provide a representation formula for viscosity solutions to a class of nonlinear second order parabolic PDE problem involving sublinear operators. This is done through a dynamic programming principle derived from [8]. The formula can be…

It is well known that for solutions of semi-linear parabolic PDEs, there are equivalent probabilistic interpretations, which yields the so called nonlinear Feymman-Kac formula. By adopting such formula, we consider in this work a novel…

This paper is an attempt to extend the notion of viscosity solution to nonlinear stochastic partial differential integral equations with nonlinear Neumann boundary condition. Using the recently developed theory on generalized backward…

It is well-known since the work of Pardoux and Peng [12] that Backward Stochastic Differential Equations provide probabilistic formulae for the solution of (systems of) second order elliptic and parabolic equations, thus providing an…

In this paper we propose a notion of viscosity solutions for path dependent semi-linear parabolic PDEs. This can also be viewed as viscosity solutions of non-Markovian backward SDEs, and thus extends the well-known nonlinear Feynman-Kac…

We provide a representation formula for viscosity solutions to a class of nonlinear second order parabolic PDEs given as a sup--envelope function. This is done through a dynamic programming principle derived from Denis, Hu, Peng (2010). The…

The classical Feynman-Kac identity represents solutions of linear partial differential equations in terms of stochastic differential euqations. This representation has been generalized to nonlinear partial differential equations on the one…

In this paper we give a new formulation of the compressible Navier-Stokes by introducing an suitable effective velocity $v=u+\n\va(\rho)$ provided that the viscosity coefficients verify the algebraic relation of \cite{BD}. We give in…

This paper investigates sufficient conditions for a Feynman-Kac functional up to an exit time to be the generalized viscosity solution of a Dirichlet problem. The key ingredient is to find out the continuity of exit operator under Skorokhod…

This paper establishes a Feynman-Kac formula to represent the solution to general time inhomogeneous stochastic parabolic partial differential equations driven by multiplicative fractional Gaussian noises in bounded domain where L_t is a…

We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that…

We prove existence and uniqueness results for solutions to a class of optimal transportation problems with infinitely many marginals, supported on the real line. We also provide a characterization of the solution with an explicit formula.…

We prove and implement stochastic solution (or Feynman-Kac) formulas for boundary value problems involving the spectral fractional Laplacian with nonzero Dirichlet boundary condition. The main tools used in the proofs are the abstract…

This paper is devoted to the study of the large time behaviour of viscosity solutions of parabolic equations with Neumann boundary conditions. This work is the sequel of [13] in which a probabilistic method was developped to show that the…

We present a general method of solving the Cauchy problem for multidimensional parabolic (diffusion type) equation with variable coefficients which depend on spatial variable but do not change over time. We assume the existence of the…

We obtain solutions of the nonlinear degenerate parabolic equation \[ \frac{\partial \rho}{\partial t} = {div} \Big\{\rho \nabla c^\star [ \nabla (F^\prime(\rho)+V) ] \Big\} \] as a steepest descent of an energy with respect to a convex…

We study stability of stationary solutions for a class of non-local semilinear parabolic equations. To this end, we prove the Feynman--Kac formula for a L\'{e}vy processes with time-dependent potentials and arbitrary initial condition. We…