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A dynamical system driven by non-Gaussian Levy 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 Levy 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 Levy noise case), in terms of the reciprocal of the small noise intensity.
In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost periodic, almost automorphic, Birkhoff recurrent, almost recurrent in the sense of Bebutov, Levitan almost periodic, pseudo-peri
In this paper we study the asymptotic properties of the power variations of stochastic processes of the type X=Y+L, where L is an alpha-stable Levy process, and Y a perturbation which satisfies some mild Lipschitz continuity assumptions. We establish
Many dynamics are random processes with increments given by a quadratic form of a fast Gaussian process. We find that the rate function which describes path large deviations can be computed from the large interval asymptotic of a certain Fredholm det
We explore the archetype problem of an escape dynamics occurring in a symmetric double well potential when the Brownian particle is driven by {it white Levy noise} in a dynamical regime where inertial effects can safely be neglected. The behavior of
Mixing rates and decay of correlations for dynamics defined by potentials with summable variations are well understood, but little is known for non-summable variations. In this paper, we exhibit upper bounds for these quantities in the case of dynami