## On reflecting Brownian motion - a weak convergence approach.(English)Zbl 0704.60081

Consider a d-dimensional domain D of finite Lebesgue measure. The authors define a certain sequence of stationary diffusion processes with drifts that tend to infinity at the boundary in such a way as to keep the sample paths in D. It is proved that this sequence is tight and any limit process is a continuous, stationary Markov process in $$\bar D$$ that can be identified with the stationary reflecting Brownian motion defined by M. Fukushima [see Osaka J. Math. 4, 183-215 (1967; Zbl 0317.60033)] using the Dirichlet form that is proportional to $$\int_{D}| \nabla g|^ 2 dx,$$ $$g\in H^ 1(D).$$
Furthermore, under a mild condition on the boundary of D, which is easily satisfied when D is a Lipschitz domain, it is shown that this process has a Skorokhod-like semimartingale representation.
Reviewer: R.Wu

### MSC:

 60J65 Brownian motion 60J60 Diffusion processes 60J45 Probabilistic potential theory

Zbl 0317.60033
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