We propose the model, which allows us to approximate fractional Levy noise and fractional Levy motion. Our model is based (i) on the Gnedenko limit theorem for an attraction basin of stable probability law, and (ii) on regarding fractional noise as the result of fractional integration/differentiation of a white Levy noise. We investigate self-affine properties of the approximation and conclude ...

We study parameter estimation for discretely observed stochastic differential equations driven by small Levy noises. There have been many applications of small noise asymptotics to mathematical finance and insurance. Using small noise models we can deal with both applications and statistical inference. We do not impose Lipschitz condition on the dispersion coefficient function and any moment co...

A random multiplicative process with additive noise is described by a Langevin equation. We show that the fluctuation-dissipation relation is satisfied in the Langevin model, if the noise strength is not so strong. keywords fluctuation-dissipation theorem, Langevin equation, multiplicative noise, Levy flight.

Based on the theory of independently scattered random measures, we introduce a natural generalisation Gaussian space-time white noise to Levy-type setting, which call Levy-valued measures. We determine subclass cylindrical Levy processes correspond and describe elements this uniquely by their characteristic function. embed measure, or corresponding process, in space general tempered distributio...

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...

Many engineering applications require extracting a signal from observations corrupted by additive noise, possibly heavy-tailed. We assume that the observation noise is a Levy process, while the signal is Gaussian, and derive a non-linear recursive filter that minimizes the L error. A sub-optimal filter is proposed for numerical purposes, and simulations show that it out-performs the existing li...

A recent paper by Patel and Kosko (2008) demonstrated stochastic resonance (SR) for general feedback continuous and spiking neuron models using additive Lévy noise constrained to have finite second moments. In this brief, we drop this constraint and show that their result extends to general LEvy noise models. We achieve this by showing that "large jump" discontinuities in the noise can be contr...

Stochastic fluctuations of coherent and incoherent components of the resonance fluorescence intensity induced by Wiener-Levy laser phase noise are investigated. Statistical properties of the atomic dipole moment and stochastic Mollow spectra of atomic dipole fluctuations for different values of the laser linewidth and Rabi frequency are calculated. It is shown that these spectra exhibit a tripl...