Probabilistic Representation of a Class of Non Conservative Nonlinear Partial Differential Equations



Anthony LECAVIL, Nadia OUDJANE and Francesco RUSSO

We introduce a new class of nonlinear Stochastic Differential Equations in the sense ofMcKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the propagation of chaos. To this system, we associate a random function which is proved to converge to a solution of a regularized version of PDE.

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