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Some results on the problem of exit from a domain

Author

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  • Bobrovsky, Ben-Zion
  • Zeitouni, Ofer

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.

Suggested Citation

  • Bobrovsky, Ben-Zion & Zeitouni, Ofer, 1992. "Some results on the problem of exit from a domain," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 241-256, June.
    • Handle: RePEc:eee:spapps:v:41:y:1992:i:2:p:241-256
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    Cited by:

    1. Han, Qun & Xu, Wei & Yue, Xiaole, 2016. "Exit location distribution in the stochastic exit problem by the generalized cell mapping method," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 302-306.

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