On diffusions that cannot escape from a convex set
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.
scientific article; zbMATH DE number 4121166