Heavy (or large) ions in a fluid in an electric field: The diffusion equation exactly following from the Fokker–Planck equation

2008 ◽  
Vol 129 (4) ◽  
pp. 044903 ◽  
Author(s):  
Leonardo Ferrari
Keyword(s):  
Diffusion Equation ◽  
Electric Field ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Supplement of differential equations of fraction order for forecasting of financial markets

2018 ◽  
Vol 170 ◽  
pp. 01075
Author(s):  
Sergey Erokhin ◽  
Olga Roshka
Keyword(s):  
Differential Equation ◽  
Diffusion Equation ◽  
Fractional Order ◽  
Capital Markets ◽  
Equity Markets ◽  
Planck Equation ◽  
Theoretical Physics ◽  
Advection Diffusion Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

In this paper, the analysis of capital markets takes place using the advection-diffusion equation. It should be noted that the methods used in modern theoretical physics have long been used in the analysis of capital markets. In particular, the Fokker-Planck equation has long been used in finding the probability density function of the return on equity. Throughout the study, a number of authors have considered the supplement of the Fokker-Planck equation in the forecasting of equity markets, as a differential equation of second order. In this paper, the first time capital markets analysis is performed using the fractional diffusion equation. The rationale is determined solely by the application nature, which consists in generation of trading strategy in equity markets with the supplement of differential equation of fractional order. As the subject for studies, the differential operator of fractional order in partial derivatives was chosen – the Fokker-Planck equation. The general solutions of equation are the basis for the forecast on the exchange rate of equities included in the Dow Jones Index Average (DJIA).

ASYMPTOTIC ANALYSIS OF THE FOKKER-PLANCK EQUATION RELATED TO BROWNIAN MOTION

1994 ◽  
Vol 04 (01) ◽  
pp. 17-33 ◽  
Author(s):  
J. BANASIAK ◽  
J.R. MIKA
Keyword(s):  
Brownian Motion ◽  
Diffusion Equation ◽  
Asymptotic Solution ◽  
Asymptotic Analysis ◽  
Collision Operator ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Expansion Procedure ◽  
The Difference ◽  
Fokker Planck

In this paper we apply the modified Chapman-Enskog expansion procedure to find the asymptotic solution of the Fokker-Planck equation related to Brownian motion. We prove that the asymptotic solution is defined by the diffusion equation and show that the difference between the exact and asymptotic solutions is of order ε2 where 1/ε is related to the magnitude of the collision operator.

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