scholarly journals THE FRACTIONAL CHAPMAN–KOLMOGOROV EQUATION

2007 ◽  
Vol 21 (04) ◽  
pp. 163-174 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Fractional Order ◽  
Planck Equation ◽  
Kolmogorov Equation ◽  
Fractional Integrals ◽  
Fractal Media ◽  
Fokker Planck Equation ◽  
Fokker Planck

The Chapman–Kolmogorov equation with fractional integrals is derived. An integral of fractional order is considered as an approximation of the integral on fractal. Fractional integrals can be used to describe the fractal media. Using fractional integrals, the fractional generalization of the Chapman–Kolmogorov equation is obtained. From the fractional Chapman–Kolmogorov equation, the Fokker–Planck equation is derived.

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).

scholarly journals FOKKER–PLANCK EQUATION FOR FRACTIONAL SYSTEMS

2007 ◽  
Vol 21 (06) ◽  
pp. 955-967 ◽  
Author(s):  
VASILY E. TARASOV
Keyword(s):  
Phase Space ◽  
Power Systems ◽  
Fractional Power ◽  
Planck Equation ◽  
Distribution Functions ◽  
Fractional Integrals ◽  
Fractional Systems ◽  
Fokker Planck Equation ◽  
Bogoliubov Equations ◽  
Fokker Planck

The normalization condition, average values, and reduced distribution functions can be generalized by fractional integrals. The interpretation of the fractional analog of phase space as a space with noninteger dimension is discussed. A fractional (power) system is described by the fractional powers of coordinates and momenta. These systems can be considered as non-Hamiltonian systems in the usual phase space. The generalizations of the Bogoliubov equations are derived from the Liouville equation for fractional (power) systems. Using these equations, the corresponding Fokker–Planck equation is obtained.

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
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