# Thermally activated traversal of an energy barrier of arbitrary shape

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By combining the maximum entropy principle with some considerations related to derivatives of fractional order, one is led to suggest a Fokkerâ€“Planck of fractional order with respect to time, which could be related to dynamical systems subject to fractional Brownian motion. The relation...

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Using the method of asymptotics, a systematic solution is developed for the velocity distribution in the boundary layer, governed by the one dimensional Fokkerâ€“Planck equation for the steady-state Brownian motion near a plane absorber. From the formal solution to the Fokkerâ€“Planck...

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In the classical analysis many models used to real data description are based on the standard Brownian diffusion-type processes. However, some real data exhibit characteristic periods of constant values. In such cases the popular systems seem not to be applicable. Therefore we propose an...

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The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with LÃ©vy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density function of LÃ©vy flights in different smooth...

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We investigate statistics of occupation times for an over-damped Brownian particle in an external force field, using a backward Fokkerï¿½Planck equation introduced by Majumdar and Comtet. For an arbitrary potential field the distribution of occupation times is expressed in terms of solutions...