Some results on the problem of exit from a domain

Ben-Zion Bobrovsky and Ofer Zeitouni

Stochastic Processes and their Applications, 1992, vol. 41, issue 2, 241-256

Abstract: The problem of exit from a domain of attraction of a stable equilibrium point in the presence of small noise is considered for a class of two-dimensional systems. It is shown that for these systems, the exit measure is 'skewed' in the sense that if S denotes the saddle point in the quasipotential towards which the exit measure collapses as the noise intensity goes to zero, then there exists an [var epsilon] dependent neighborhood [Delta] of S such that lim P(exit in [Delta])/|[Delta]|=0. Thus, the most probable exit point is not S but is rather skewed aside by [var epsilon][gamma] for some [gamma]. The behaviour of such skewness, which was predicted by asymptotic expansions, depends on the ratio of normal to tangential forces around the saddle point.

Keywords: exit; problem; large; deviations; characteristic; boundary; two-dimensional; diffusions; asymptotic; expansions (search for similar items in EconPapers)
Date: 1992
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