On the enhancement of diffusion by chaos, escape rates and stochastic instability

Collet, Pierre; Martínez, Servet; Schmitt, Bernard

doi:10.1090/S0002-9947-99-02023-1

On the enhancement of diffusion by chaos, escape rates and stochastic instability
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by Pierre Collet, Servet Martínez and Bernard Schmitt

Trans. Amer. Math. Soc. 351 (1999), 2875-2897

DOI: https://doi.org/10.1090/S0002-9947-99-02023-1

Published electronically: March 8, 1999

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Abstract:

We consider stochastic perturbations of expanding maps of the interval where the noise can project the trajectory outside the interval. We estimate the escape rate as a function of the amplitude of the noise and compare it with the purely diffusive case. This is done under a technical hypothesis which corresponds to stability of the absolutely continuous invariant measure against small perturbations of the map. We also discuss in detail a case of instability and show how stability can be recovered by considering another invariant measure.

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