CRISAN , Dan

The paper is a continuation of the Kusuoka-Stroock programme of establishing smoothness properties of solutions of (possibly) degenerate partial differential equations by using probabilistic methods. We analyze here a class of semi-linear parabolic partial differential equations for which the linear part is a second order differential operator...

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We analyze a simple macroscopic model describing the evolution of a cloud of particles confined in a magneto-optical trap. The behavior of the particles is mainly driven by self–consistent attractive forces. In contrast to the standard model of gravitational forces, the force field does not result from a potential; moreover, the non linear...

This paper is dedicated to the presentation and the analysis of a numerical scheme for forward-backward SDEs of the McKean-Vlasov type, or equivalently for solutions to PDEs on the Wasserstein space. Because of the mean field structure of the equation, earlier methods for classical forward-backward systems fail. The scheme is based on a...

We analyze a class of nonlinear partial dierential equations (PDEs) defined on the Euclidean space of dimension d times the Wasserstein space of d-dimensional probability measures with a finite second-order moment. We show that such equations admit a classical solutions for sufficiently small time intervals. Under additional constraints, we...