Probability calculus of fractional order and fractional Taylor’s series application to Fokker–Planck equation and information of non-random functions

2009 ◽  
Vol 40 (3) ◽  
pp. 1428-1448 ◽  
Author(s):  
Guy Jumarie
Keyword(s):  
Fractional Order ◽  
Planck Equation ◽  
Probability Calculus ◽  
Random Functions ◽  
Fokker Planck Equation ◽  
Fractional Taylor’S Series ◽  
Taylor’S Series ◽  
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).

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.

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

scholarly journals Time-changed fractional Ornstein-Uhlenbeck process

2020 ◽  
Vol 23 (2) ◽  
pp. 450-483 ◽  
Author(s):  
Giacomo Ascione ◽  
Yuliya Mishura ◽  
Enrica Pirozzi
Keyword(s):  
Planck Equation ◽  
Uhlenbeck Process ◽  
Fokker Planck Equation ◽  
Ornstein Uhlenbeck Process ◽  
Fokker Planck

AbstractWe define a time-changed fractional Ornstein-Uhlenbeck process by composing a fractional Ornstein-Uhlenbeck process with the inverse of a subordinator. Properties of the moments of such process are investigated and the existence of the density is shown. We also provide a generalized Fokker-Planck equation for the density of the process.

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