Analytical solution of stochastic differential equation by multilayer perceptron neural network approximation of Fokker–Planck equation

2019 ◽  
Vol 36 (3) ◽  
pp. 637-653 ◽  
Author(s):  
Ali Namadchian ◽  
Mehdi Ramezani
Keyword(s):  
Neural Network ◽  
Differential Equation ◽  
Analytical Solution ◽  
Stochastic Differential Equation ◽  
Multilayer Perceptron ◽  
Planck Equation ◽  
Fokker Planck Equation ◽  
Fokker Planck

scholarly journals Fractional Fokker-Planck-Kolmogorov equations associated with SDES on a bounded domain

2017 ◽  
Vol 20 (5) ◽  
Author(s):  
Sabir Umarov
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Stochastic Differential Equation ◽  
Bounded Domain ◽  
Planck Equation ◽  
Initial Boundary ◽  
Order Differential Operator ◽  
Fokker Planck Equation ◽  
Initial Boundary Value ◽  
Fokker Planck

AbstractThis paper is devoted to the fractional generalization of the Fokker-Planck equation associated with a nonlinear stochastic differential equation on a bounded domain. The driving process of the stochastic differential equation is a Lévy process subordinated to the inverse of Lévy’s mixed stable subordinators. The Fokker-Planck equation is given through the general Waldenfels operator, while the boundary condition is given through the general Wentcel’s boundary condition. As a fractional operator a distributed order differential operator with a Borel mixing measure is considered. In the paper fractional generalizations of the Fokker-Planck equation are derived and the existence of a unique solution of the corresponding initial-boundary value problems is proved.

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).

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