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

Xiao Wang, Wenpeng Shang, Xiaofan Li, Jinqiao Duan, Yanghong Huang
2018 arXiv   pre-print
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]

D. Schertzer, M. Larchevêque (LMM, Université Pierre et Marie Curie, Paris, France), J. Duan (Illinois Institute of Technology, Chicago, USA), V.V. Yanovsky (Turbulence Research, National Acad. Sci. Ukraine, Kharkov, Ukraine) S. Lovejoy (Physics Department, McGill University, Montreal, Quebec (+1 others)
2000 arXiv   pre-print
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

D. Schertzer, M. Larchevêque, J. Duan, V. V. Yanovsky, S. Lovejoy
2001 Journal of Mathematical Physics  
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

B. Dybiec, E. Gudowska-Nowak, I. M. Sokolov
2007 Physical Review E  
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]

Tomasz Srokowski
2011 arXiv   pre-print
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  
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]

Krzysztof Szczepaniec, Bartlomiej Dybiec
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 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

S. I. Denisov, Werner Horsthemke, Peter Hänggi
2008 Physical Review E  
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]

Yanjie Zhang, Xiao Wang, Qiao Huang, Jinqiao Duan, Tingting Li
2020 arXiv   pre-print
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

E.A. Abdel-Rehim, R. Gorenflo
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.  ... 
doi:10.1016/j.cam.2007.10.052 fatcat:dz5opiny3zhxjiase2u75hehq4

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

Krzysztof Szczepaniec, Bartłomiej Dybiec
2014 Physical Review E  
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

B. Dybiec, E. Gudowska-Nowak, P. Hänggi
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] .  ... 
doi:10.1103/physreve.73.046104 pmid:16711875 fatcat:hauvc7zvvzav5auokvpb7pmyue

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

Bartłomiej Dybiec, Ewa Gudowska-Nowak
2010 Chaos  
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]

Jinqiao Duan, Hui Wang
2018 arXiv   pre-print
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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