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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...

Phase transition and Martin boundary

Hans Föllmer (1975)

Séminaire de probabilités de Strasbourg

Poisson boundary of triangular matrices in a number field

Bruno Schapira (2009)

Annales de l’institut Fourier

The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary of random rational affinities.

Potential theory for the α-stable Schrödinger operator on bounded Lipschitz domains

Krzysztof Bogdan, Tomasz Byczkowski (1999)

Studia Mathematica

The purpose of the paper is to extend results of the potential theory of the classical Schrödinger operator to the α-stable case. To obtain this we analyze a weak version of the Schrödinger operator based on the fractional Laplacian and we prove the Conditional Gauge Theorem.

Predictable local times and exit systems

Haya Kaspi, Bernard Maisonneuve (1986)

Séminaire de probabilités de Strasbourg

Probabilistic Approach to the Neumann Problem for a Symmetric Operator

Benchérif-Madani, Abdelatif (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: Primary 60J45, 60J50, 35Cxx; Secondary 31Cxx.We give a probabilistic formula for the solution of a non-homogeneous Neumann problem for a symmetric nondegenerate operator of second order in a bounded domain. We begin with a g-Hölder matrix and a C^1,g domain, g > 0, and then consider extensions. The solutions are expressed as a double layer potential instead of a single layer potential; in particular a new boundary function is discovered and boundary random...