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On diffusions that cannot escape from a convex set. (English) Zbl 0684.60059
Let X be a diffusion on an open, convex, bounded domain D in $${\mathbb{R}}^ d$$. The drift term of X is assumed to be of the form $$\nabla f/f$$ where $$f\in C'(D)$$, $$f>0$$ on D, radial close to $$\partial D$$, and vanishes on $$\partial D$$. It is seen that Khasminskij’s test for nonexplosion takes here the simple form $$\int_{D}(1/f(y))dy=\infty$$. This result is applied to derive a large deviation result for Brownian occupation measures.
Reviewer: P.Salminen

##### MSC:
 60J60 Diffusion processes 60F10 Large deviations
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##### References:
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