A Two-Dimensional Oblique Extension of Bessel Processes

D. Lepingle

2017, v.23, №2, 233-266

ABSTRACT

We consider a Brownian motion forced to stay in the quadrant by an electrostatic oblique repulsion from the sides. We tackle the question of hitting the corner
or an edge, and find product-form stationary measures under a certain condition, which is reminiscent of the skew-symmetry condition for a reflected Brownian motion.

Keywords: singular stochastic differential equation; electrostatic repulsion; Bessel process; product form stationary distribution; skew-symmetry condition; obliquely reflected Brownian motion

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