论文信息 - On Time-Reversal of Reflected Brownian Motions

On Time-Reversal of Reflected Brownian Motions

In this paper, a partial converse of a previous result on time-reversal of reflected Brownian motions is proved. Indeed, from [11], the time-reversal of a stationary reflected Brownian motion in a simple polyhedral domain is again a reflected Brownian motion if the directions of reflection satisfy a certain skew symmetry condition, and in this case the stationary distribution has a separable density. A converse of this result is proved here for a certain class of reflected Brownian motions in polyhedral domains that arise in applications to queueing theory. Before elaborating on this, some background on time-reversal of reflected Brownian motions is provided in the following paragraph.

Ruth J. Williams

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