Positivity theorem for a general manifold.

Rémi Léandre

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Malliavin Calculus for a general manifold

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Stochastic Poisson-Sigma model

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We produce a stochastic regularization of the Poisson-Sigma model of Cattaneo-Felder, which is an analogue regularization of Klauder’s stochastic regularization of the hamiltonian path integral [23] in field theory. We perform also semi-classical limits.

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Stochastic differential inclusions of Langevin type on Riemannian manifolds

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We introduce and investigate a set-valued analogue of classical Langevin equation on a Riemannian manifold that may arise as a description of some physical processes (e.g., the motion of the physical Brownian particle) on non-linear configuration space under discontinuous forces or forces with control. Several existence theorems are proved.

SPDEs with pseudodifferential generators: the existence of a density

Samy Tindel (2000)

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We consider the equation du(t,x)=Lu(t,x)+b(u(t,x))dtdx+σ(u(t,x))dW(t,x) where t belongs to a real interval [0,T], x belongs to an open (not necessarily bounded) domain $𝒪$ , and L is a pseudodifferential operator. We show that under sufficient smoothness and nondegeneracy conditions on L, the law of the solution u(t,x) at a fixed point $(t, x) \in [0, T] \times 𝒪$ is absolutely continuous with respect to the Lebesgue measure.