Product-form invariant measures for Brownian motion with drift satisfying a skew-symmetry type condition

Details Product-form invariant measures for Brownian motion with drift satisfying a skew-symmetry type condition Product-form invariant measures for Brownian motion with drift satisfying a skew-symmetry type condition

2012-01-26

arxiv.org/abs/1201.5586v2

Mathematics

Probability

Scientific paper

Motivated by recent developments on positive-temperature polymer models we propose a generalisation of reflected Brownian motion (RBM) in a polyhedral domain. Our process is obtained by replacing the singular drift on the boundary by a continuous one which depends, via a potential $U$, on the position of the process relative to the domain. We show that our generalised process has an invariant measure in product form if and only if we have a certain skew-symmetry condition that is independent of the choice of potential. Applications include examples motivated by queueing theory, Brownian motion with rank-dependent drift and a process with close connections to the $\delta$-Bose gas.

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