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Fokker-Planck equation driven by asymmetric Lévy motion
[article]

2018
*
arXiv
*
pre-print

In this work, we consider the

arXiv:1803.00923v1
fatcat:rlmwb24q3ng3xfasr3dlr6amja
*Fokker*-*Planck**equation*(FPE) due to one-dimensional*asymmetric**Lévy**motion*, which is a nonlocal partial differential*equation*. ... Our numerical method is validated*by*comparing with exact solutions for special cases. ... Acknowledgements The research is partially supported*by*the grants China Scholarship Council #201306160071 (X.W.), NSF-DMS #1620449 (J.D. and X.L.), National Natural Science Foundation of China grants ...##
###
Fractional Fokker-Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
[article]

2000
*
arXiv
*
pre-print

We therefore derive in this paper a Fractional

arXiv:chao-dyn/9912004v2
fatcat:rvznd4cubnhdpbe457lifaqqii
*Fokker*-*Planck**equation*for the probability distribution of particles whose*motion*is governed*by*a nonlinear Langevin-type*equation*, which is*driven**by*a ... The*Fokker*-*Planck**equation*has been very useful for studying dynamic behavior of stochastic differential*equations**driven**by*Gaussian noises. ...*equations**driven**by**Levy*stable noises. ...##
###
Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises

2001
*
Journal of Mathematical Physics
*

In this paper, we derive a Fractional

doi:10.1063/1.1318734
fatcat:n3kd3bsdrrewdg3lztfzs6hami
*Fokker*--*Planck**equation*for the probability distribution of particles whose*motion*is governed*by*a nonlinear Langevin-type*equation*, which is*driven**by*a non-Gaussian ... The*Fokker*-*Planck**equation*has been very useful for studying dynamic behavior of stochastic differential*equations**driven**by*Gaussian noises. ...*equations**driven**by**Lévy*stable noises. ...##
###
Stationary states in Langevin dynamics under asymmetric Lévy noises

2007
*
Physical Review E
*

Properties of systems

doi:10.1103/physreve.76.041122
pmid:17994951
fatcat:qtrssl66prdabnzbmowfzejh6u
*driven**by*white non-Gaussian noises can be very different from these systems*driven**by*the white Gaussian noise. ... We investigate stationary probability densities for systems*driven**by*α-stable*Lévy*type noises, which provide natural extension to the Gaussian noise having however a new property mainly a possibility ... The support*by*DFG within SFB 555 is also acknowledged. ...##
###
Correlated Lévy noise in linear dynamical systems
[article]

2011
*
arXiv
*
pre-print

The

arXiv:1005.0301v2
fatcat:7nizxecvmfh7zauqmbua5wbnzu
*Fokker*-*Planck**equation**driven**by*that noise is solved. Distributions have the*Levy*shape and their width, for a given time, is smaller than for processes in the white noise limit. ... Linear dynamical systems,*driven**by*a non-white noise which has the*Levy*distribution, are analysed. ... If jumps are*Lévy*distributed, the*Fokker*-*Planck**equation*is fractional both in time and position. ...##
###
Page 4997 of Mathematical Reviews Vol. , Issue 2004f
[page]

2004
*
Mathematical Reviews
*

Cahn-Hilliard

*equation*, whose large-time behavior corresponds to*motion**by*surface diffusion. ... Our analysis is based on a novel generalization of the*Fokker*-*Planck**equation*suitable for systems in thermal equilibrium. ...##
###
Escape from bounded domains driven by multi-variate α-stable noises
[article]

2015
*
arXiv
*
pre-print

In this paper we provide an analysis of a mean first passage time problem of a random walker subject to a bi-variate α-stable

arXiv:1406.7096v3
fatcat:4z6rhuei4nhnrj3qpyyctkhnfi
*Lévy*type noise from a 2-dimensional disk. ... appropriate choice of parameters the mean first passage time reveals non-trivial, non-monotonous dependence on the stability index α describing jumps' length asymptotics both for spherical and Cartesian*Lévy*... ACKNOWLEDGMENTS This project has been supported in part*by*the grant from National Science Center (2014/13/B/ST2/020140). ...##
###
Steady-state Lévy flights in a confined domain

2008
*
Physical Review E
*

We derive the generalized

doi:10.1103/physreve.77.061112
pmid:18643222
fatcat:7i62ylg7cvbuhpib6s5xlp22pu
*Fokker*-*Planck**equation*associated with a Langevin*equation**driven**by*arbitrary additive white noise. ... The fractional*Fokker*-*Planck**equation*for*Lévy*flights is derived and solved analytically in the steady state. ... A10, and*by*the German Excellence Cluster "Nanosystems Initiative Munich" ͑NIM͒. ...##
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Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative α-stable noises
[article]

2020
*
arXiv
*
pre-print

The

arXiv:1811.05610v5
fatcat:pxeqcdtrmvemvjyjmjtzwksw24
*Fokker*-*Planck**equations*(FPEs) for stochastic systems*driven**by*additive symmetric α-stable noises may not adequately describe the time evolution for the probability densities of solution paths in ... A finite difference method for solving the nonlocal*Fokker*-*Planck**equation*(FPE) is constructed, which is shown to satisfy the discrete maximum principle and to be convergent. ... the SDEs*driven**by*multiplicative*asymmetric*one-dimensional*Lévy**motions*and derive the corresponding FPEs. ...##
###
Simulation of the continuous time random walk of the space-fractional diffusion equations

2008
*
Journal of Computational and Applied Mathematics
*

*Fokker*-

*Planck*

*equation*which is useful in studying the dynamic behaviour of stochastic differential

*equations*

*driven*

*by*the non-Gaussian (

*Lévy*) noises. ...

*Lévy*distribution, 0 < α < 2. ... The

*Fokker*-

*Planck*

*equation*(FPE) is one of the most widely used

*equations*of statistical physics for studying the dynamic behaviour of stochastic differential

*equations*

*driven*

*by*the Gaussian noises. ...

##
###
Stationary states in two-dimensional systems driven by bivariate Lévy noises

2014
*
Physical Review E
*

Here, it is demonstrated that 2D systems

doi:10.1103/physreve.90.032128
pmid:25314416
fatcat:ezuw7xpx7fbo5lspvorbrbakcq
*driven**by*bi-variate α-stable noises are even more surprising than their 1D analogs. ... Consequently, 2D systems are described*by*a whole family of Langevin and fractional diffusion*equations*. Solutions of these*equations*bear some common properties but also can be very different. ... Consequently, the 2D systems*driven**by*bi-variate α-stable noises are described*by*the whole family of Langevin*equations*and associated fractional Smoluchowski-*Fokker*-*Planck**equations*depending on the ...##
###
Lévy-Brownian motion on finite intervals: Mean first passage time analysis

2006
*
Physical Review E
*

*driven*

*by*Gaussian white noise. ... We present the analysis of the first passage time problem on a finite interval for the generalized Wiener process that is

*driven*

*by*

*Lévy*stable noises. ... The same information can be also obtained

*by*use of the method of images or

*by*solving the corresponding, local boundary value problem of the diffusive

*Fokker*-

*Planck*

*equation*[8, 9] . ...

##
###
Page 4195 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

The

*Fokker*-*Planck**equation*describing the evolution of the probability density function of X(t) is given in terms of the drift function and the jump mea- sure of the*Lévy*process. ... In this way the Laplace operator in the*Fokker*-*Planck**equation*for the Gaussian case is replaced*by*an integro-differential operator arising from the pure jump driver L. ...##
###
Subordinated diffusion and continuous time random walk asymptotics

2010
*
Chaos
*

Anomalous transport is usually described either

doi:10.1063/1.3522761
pmid:21198099
fatcat:jimlq4oam5bhxi4rzhjlohfuey
*by*models of continuous time random walks (CTRW) or, otherwise*by*fractional*Fokker*-*Planck**equations*(FFPE). ... The other is based on a discretized form of a subordinated Langevin*equation*in which the physical time defined via the number of subsequent steps of*motion*is itself a random variable. ... ACKNOWLEDGMENTS This project has been supported in part (EGN)*by*...##
###
Geometric Methods for Stochastic Dynamical Systems
[article]

2018
*
arXiv
*
pre-print

As the solution of the

arXiv:1811.00723v1
fatcat:4ikqbpdvdzcs3jr76typblxnou
*Fokker*-*Planck**equation*, the probability density function p(x, t) is a surface in the (x, t, p)-space. ... Mean phase portraits Given the probability density function p(x, t) p(x, t|x 0 , 0) as the solution of the*Fokker*-*Planck**equation*(6). ...
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