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Boundary behavior of a constrained brownian motion between reflecting-repellent walls

Lépingle D.

Probability and Mathematical Statistics

2010

Vol. 30, Fasc. 2

273--287

Stochastic variational inequalities provide a unified treatment for stochastic differential equations living in a closed domain with normal reflection and/or singular repellent drift. When the domain is a convex polyhedron, we prove that the reflected-repelled Brownian motion does not hit the non-smooth part of the boundary. A sufficient condition for nonhitting a face of the polyhedron is derived from the one-dimensional situation. A full answer to the question of attainability of the walls of the Weyl chamber may be given for a radial Dunkl process.

Large deviations for wishart processes

Donati-Martin C.

Probability and Mathematical Statistics

2008

Vol. 28, Fasc. 2

325--343

Let Xδ be a Wishart process of dimension δ, with values in the set of positive matrices of size m. We are interested in the large deviations for a family of matrix-valued processes {δ−1X(δ)t ; t ≤1} as δ tends to infinity. The process X(δ) is a solution of a stochastic differential equation with a degenerate diffusion coefficient. Our approach is based upon the introduction of exponential martingales. We give some applications to large deviations for functionals of the Wishart processes, for example the set of eigenvalues.