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Characterization of stationary distributions of reflected diffusions. (English) Zbl 1306.60111

The authors establish a characterization of stationary distributions for a class of reflected diffusions in piecewise smooth domains with oblique reflection. A precise form of the pertinent submartingale problem is provided, and the existence of a stationary distribution for reflected diffusion in a bounded domain is deduced. There is a good discussion of earlier work, and relevant illustrative examples are given.

MSC:

60J60 Diffusion processes
60J65 Brownian motion
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60K25 Queueing theory (aspects of probability theory)
90B15 Stochastic network models in operations research
90B22 Queues and service in operations research
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