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On time-reversal of reflected Brownian motions. (English) Zbl 0653.60069

Stochastic processes, Semin., Princeton/New Jersey 1987, Prog. Probab. Stat. 15, 265-276 (1988).
[For the entire collection see Zbl 0635.00011.]
The author has shown in Probab. Theory Relat. Fields 75, 459-485 (1987; Zbl 0608.60074) that 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.
Reviewer: R.J.Williams

MSC:

60J60 Diffusion processes
60J65 Brownian motion