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Brownian motion in the quadrant with oblique repulsion from the sides

We consider the problem of strong existence and uniqueness of a Brownian motion forced to stay in the quadrant by an electrostatic repulsion from the sides that works obliquely. The results are reminiscent of the study of a Brownian motion with oblique reflection in a wedge. Actually, the same skew symmetry condition is involved when looking for a stationary distribution in product form. the terms of the product are now gamma distributions in place of exponential ones. An associate purely deterministic problem is also considered.

preprint2013arXivOpen access
Dominique Lépingle
math.PR
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Dominique Lépingle

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