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Invariance principle for the random conductance model with dynamic bounded conductances

Sebastian Andres — 2014

Annales de l'I.H.P. Probabilités et statistiques

We study a continuous time random walk X in an environment of dynamic random conductances in ℤ d . We assume that the conductances are stationary ergodic, uniformly bounded and bounded away from zero and polynomially mixing in space and time. We prove a quenched invariance principle for X , and obtain Green’s functions bounds and a local limit theorem. We also discuss a connection to stochastic interface models.

Pathwise differentiability for SDEs in a convex polyhedron with oblique reflection

Sebastian Andres — 2009

Annales de l'I.H.P. Probabilités et statistiques

In this paper, the object of study is a Skorohod SDE in a convex polyhedron with oblique reflection at the boundary. We prove that the solution is pathwise differentiable with respect to its deterministic starting point up to the time when two of the faces are hit simultaneously. The resulting derivatives evolve according to an ordinary differential equation, when the process is in the interior of the polyhedron, and they are projected to the tangent space, when the process hits the boundary, while...

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