The first boundary exit point of a diffusion process with small diffusion

A. D. Venttsel'

M. V. Lomonosov Moscow State University

Abstract: A diffusion process with a drift $b(x)$ and small diffusion sooner or later reaches the boundary of a region containing a stable position of equilibrium of the dynamical system $\dot x_t=b(x_t)$. The first exit point belongs to a small part of the boundary (see [1, 2]). An estimate of the order of the size of this part is given.

UDC: 519

Received: 28.02.1977

 English version: Mathematical Notes, 1977, 22:3, 720–725

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