0000000000425266

AUTHOR

Bartłomiej Dybiec

0000-0002-6540-3906

showing 2 related works from this author

Statistics of residence time for Lévy flights in unstable parabolic potentials

2020

We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.

Steady stateSettore FIS/02 - Fisica Teorica Modelli E Metodi Matematicinoise-enhanced stability nonlinear relaxation time stochastic processes Lévy noiseMarkov process01 natural sciencesStability (probability)010305 fluids & plasmasNonlinear systemsymbols.namesakeLévy flight0103 physical sciencessymbolsConditional probability densityStatistical physicsDiffusion (business)010306 general physicsResidence time (statistics)Mathematics
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Spectral characteristics of steady-state Lévy flights in confinement potential profiles

2016

The steady-state correlation characteristics of superdiffusion in the form of Levy flights in one-dimensional confinement potential profiles are investigated both theoretically and numerically. Specifically, for Cauchy stable noise we calculate the steady-state probability density function for an infinitely deep rectangular potential well and for a symmetric steep potential well of the type U(x)∞x2m. For these potential profiles and arbitrary Levy index α, we obtain the asymptotic expression of the spectral power density.

Statistics and Probabilityrigorous results in statistical mechanicSettore FIS/02 - Fisica Teorica Modelli E Metodi MatematiciSteady stateMathematical analysisCauchy distributionstochastic processes (theory)Statistical and Nonlinear PhysicsProbability density functionrigorous results in statistical mechanics; stochastic particle dynamics; stochastic processes (theory); Statistical and Nonlinear Physics; Statistics and Probability; Statistics Probability and UncertaintyType (model theory)01 natural sciencesNoise (electronics)010305 fluids & plasmasstochastic particle dynamicLévy flight0103 physical sciencesStatistics Probability and Uncertainty010306 general physicsStatistical and Nonlinear PhysicPower densityMathematicsJournal of Statistical Mechanics: Theory and Experiment
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