Open AccessSOME APPLICATION OF THE FOKKER-PLANCK EQUATION
Author(s) -
Victor Grigorevich Pirozhkov,
Olga Roshka,
Temirkhan Aleroev
Publication year - 2017
Publication title -
vestnik mgsu
Language(s) - English
Resource type - Journals
eISSN - 2304-6600
pISSN - 1997-0935
DOI - 10.22227/1997-0935.2017.7.809-821
Subject(s) - mathematics , fractal , hurst exponent , continuous time random walk , currency , statistical physics , volatility (finance) , foreign exchange market , mathematical analysis , mathematical economics , econometrics , random walk , economics , statistics , physics , monetary economics
In this paper, we study the foreign exchange rates of a pair Russian ruble/US dollar on the subject of fractality. It has been shown that the time series studied quotes has the basic fractal properties. With the help of the Hurst exponent was calculated by the Hausdorff dimension, which was a fractional number that supports the hypothesis of fractality. Volatility charts were compared with charts of known solutions of the fractional differential equation wandering point particle in a self-similar fractal set. The solution of this equation is a function of Mittag-Leffler. It is shown that graphs of the Mittag-Leffler function repeat exactly the structure of graphs volatilities for different periods of time. The solution of such an equation is written out using the Mittag-Leffler functions. The graphs of these decisions are compared with the volatility charts for different time periods. It also clearly confirms that the Russian currency market is a fractal. Thus, these results will help in predicting market behavior in advance a preset time in the future, which is almost a valuable tool for working with Russian currency market.