Noise-induced jumping between metastable states in a potential depends on the structure of the noise. For an alpha-stable noise, jumping triggered by single extreme events contributes to the transition probability. This is also called Levy flights and might be of importance in triggering sudden changes in geophysical flow and perhaps even climatic changes. The steady-state statistics is also in...

we present a numerical study of a one-dimensional version of the burridge-knopoff model [16] of n-site chain of spring-blocks with stick-slip dynamics. our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. it is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...

In this paper, we use a unified framework to study Poisson stable (including stationary, periodic, quasi-periodic, almost automorphic, Birkhoff recurrent, recurrent in the sense of Bebutov, Levitan pseudo-periodic, pseudo-recurrent and stable) solutions for semilinear stochastic differential equations driven by infinite dimensional Lévy noise with large jumps. Under suitable conditions on drift...

In this paper we describe on-line Bayesian filtering methods for time series models with heavy-tailed α-stable noise. The filtering methodology is based on a scale mixtures of normals (SMiN) representation of the α-stable distribution, which reexpresses the intractable stable distribution in a conditionally Gaussian form. We describe how the method can be used for estimation of TVAR signals bur...

The representation of α-stable distributions as scale mixture of normals is exploited to model the noise in musical audio recordings. Markov Chain Monte Carlo inference is used to estimate the clean signal model and the α-stable noise model parameters in a sparse linear regression framework with structured priors. The musical audio recordings were processed both as a whole and in segments by us...