6533b862fe1ef96bd12c60e8

RESEARCH PRODUCT

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

Pierre ColletServet MartínezBernard Schmitt

subject

AmplitudeApplied MathematicsGeneral MathematicsCalculusTrajectoryInvariant measureInterval (mathematics)Statistical physicsAbsolute continuityNoise (electronics)Stability (probability)InstabilityMathematics

description

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.

yearjournalcountryeditionlanguage
1999-03-08Transactions of the American Mathematical Society
https://doi.org/10.1090/s0002-9947-99-02023-1