scholarly journals Simulation and Parametric Inference of a Mixed Effects Model with Stochastic Differential Equations Using the Fokker-Planck Equation Solution

2020 ◽  
Author(s):  
Bakrim Fadwa ◽  
Hamid El Maroufy ◽  
Hassan Ait Mousse
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Planck Equation ◽  
Mixed Effects ◽  
Mixed Effects Model ◽  
Parametric Inference ◽  
Equation Solution ◽  
Fokker Planck Equation ◽  
Fokker Planck

A method for the calculation of characteristics for the solution to stochastic differential equations

2017 ◽  
Vol 23 (3) ◽  
Author(s):  
Alexander Egorov ◽  
Victor Malyutin
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Probability Function ◽  
Transition Probability ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Transition Probability Function ◽  
Fokker Planck

AbstractIn this work, a new numerical method to calculate the characteristics of the solution to stochastic differential equations is presented. This method is based on the Fokker–Planck equation for the transition probability function and the representation of the transition probability function by means of eigenfunctions of the Fokker–Planck operator. The results of the numerical experiments are presented.

Governing equations for probability densities of Marcus stochastic differential equations with Lévy noise

2016 ◽  
Vol 17 (05) ◽  
pp. 1750033 ◽  
Author(s):  
Xu Sun ◽  
Xiaofan Li ◽  
Yayun Zheng
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Probability Density ◽  
Lévy Processes ◽  
Planck Equation ◽  
Levy Processes ◽  
Stochastic Dynamical Systems ◽  
Non Gaussian ◽  
Fokker Planck Equations ◽  
Fokker Planck

Marcus stochastic differential equations (SDEs) often are appropriate models for stochastic dynamical systems driven by non-Gaussian Lévy processes and have wide applications in engineering and physical sciences. The probability density of the solution to an SDE offers complete statistical information on the underlying stochastic process. Explicit formula for the Fokker–Planck equation, the governing equation for the probability density, is well-known when the SDE is driven by a Brownian motion. In this paper, we address the open question of finding the Fokker–Planck equations for Marcus SDEs in arbitrary dimensions driven by non-Gaussian Lévy processes. The equations are given in a simple form that facilitates theoretical analysis and numerical computation. Several examples are presented to illustrate how the theoretical results can be applied to obtain Fokker–Planck equations for Marcus SDEs driven by Lévy processes.

AN APPLICATION OF FOKKER–PLANCK EQUATION TO JOSEPHSON JUNCTION

1989 ◽  
Vol 9 (1) ◽  
pp. 109-120
Author(s):  
G. Liao ◽  
A.F. Lawrence ◽  
A.T. Abawi
Keyword(s):  
Josephson Junction ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

The Fokker-Planck equation

1998 ◽  
Vol 168 (4) ◽  
pp. 475 ◽  
Author(s):  
A.I. Olemskoi
Keyword(s):  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck
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