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Fokker-Planck equation driven by asymmetric Lévy motion
[article]
2018
arXiv
pre-print
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In this work, we consider the 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 ...
arXiv:1803.00923v1
fatcat:rlmwb24q3ng3xfasr3dlr6amja
Fractional Fokker-Planck Equation for Nonlinear Stochastic Differential Equations Driven by Non-Gaussian Levy Stable Noises
[article]
2000
arXiv
pre-print
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We therefore derive in this paper a Fractional 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. ...
arXiv:chao-dyn/9912004v2
fatcat:rvznd4cubnhdpbe457lifaqqii
Fractional Fokker–Planck equation for nonlinear stochastic differential equations driven by non-Gaussian Lévy stable noises
2001
Journal of Mathematical Physics
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In this paper, we derive a Fractional 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. ...
doi:10.1063/1.1318734
fatcat:n3kd3bsdrrewdg3lztfzs6hami
Stationary states in Langevin dynamics under asymmetric Lévy noises
2007
Physical Review E
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2007 accepted arXiv:cond-mat/0702182v2 fatcat:xsumvhb7cvhipbqbmczedjgzquOther Versions
Properties of systems 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. ...
doi:10.1103/physreve.76.041122
pmid:17994951
fatcat:qtrssl66prdabnzbmowfzejh6u
Correlated Lévy noise in linear dynamical systems
[article]
2011
arXiv
pre-print
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The 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. ...
arXiv:1005.0301v2
fatcat:7nizxecvmfh7zauqmbua5wbnzu
Page 4997 of Mathematical Reviews Vol. , Issue 2004f
[page]
2004
Mathematical Reviews
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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
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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 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). ...
arXiv:1406.7096v3
fatcat:4z6rhuei4nhnrj3qpyyctkhnfi
Steady-state Lévy flights in a confined domain
2008
Physical Review E
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We derive the generalized 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. ...
doi:10.1103/physreve.77.061112
pmid:18643222
fatcat:7i62ylg7cvbuhpib6s5xlp22pu
Numerical analysis and applications of Fokker-Planck equations for stochastic dynamical systems with multiplicative α-stable noises
[article]
2020
arXiv
pre-print
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The 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. ...
arXiv:1811.05610v5
fatcat:pxeqcdtrmvemvjyjmjtzwksw24
Simulation of the continuous time random walk of the space-fractional diffusion equations
2008
Journal of Computational and Applied Mathematics
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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. ...
doi:10.1016/j.cam.2007.10.052
fatcat:dz5opiny3zhxjiase2u75hehq4
Stationary states in two-dimensional systems driven by bivariate Lévy noises
2014
Physical Review E
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2014 pre-print arXiv:1406.7103v1 fatcat:2z5tsqmibjdnlbvzn5pegodu64
Here, it is demonstrated that 2D systems 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 ...
doi:10.1103/physreve.90.032128
pmid:25314416
fatcat:ezuw7xpx7fbo5lspvorbrbakcq
Lévy-Brownian motion on finite intervals: Mean first passage time analysis
2006
Physical Review E
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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] . ...
doi:10.1103/physreve.73.046104
pmid:16711875
fatcat:hauvc7zvvzav5auokvpb7pmyue
Page 4195 of Mathematical Reviews Vol. , Issue 2004e
[page]
2004
Mathematical Reviews
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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
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2010 pre-print arXiv:1007.3022v2 fatcat:xm7r4ankkvhmzeiv7ptm3hffpuOther Versions
Anomalous transport is usually described either 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 ...
doi:10.1063/1.3522761
pmid:21198099
fatcat:jimlq4oam5bhxi4rzhjlohfuey
Geometric Methods for Stochastic Dynamical Systems
[article]
2018
arXiv
pre-print
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As the solution of the 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). ...
arXiv:1811.00723v1
fatcat:4ikqbpdvdzcs3jr76typblxnou
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