An intermediate regime for exit phenomena driven by non-Gaussian Levy noises

Mathematics – Dynamical Systems

Scientific paper

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Stochastics and Dynamics, to appear, Vol 8, No 3, 2008

Scientific paper

A dynamical system driven by non-Gaussian L\'evy noises of small intensity is considered. The first exit time of solution orbits from a bounded neighborhood of an attracting equilibrium state is estimated. For a class of non-Gaussian L\'evy noises, it is shown that the mean exit time is asymptotically faster than exponential (the well-known Gaussian Brownian noise case) but slower than polynomial (the stable L\'evy noise case), in terms of the reciprocal of the small noise intensity.

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