Article
An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations
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Abstract
In this study, a new method to obtain approximate probability density function (pdf) of random variable of solution of stochastic differential equations (SDEs) by using generalized entropy optimization methods (GEOM) is developed. By starting given statistical data and Euler–Maruyama (EM) method approximating SDE are constructed several trajectories of SDEs. The constructed trajectories allow to obtain random variable according to the fixed time. An application of the newly developed method includes SDE model fitting on weekly closing prices of Honda Motor Company stock data between 02 July 2018 and 25 March 2019.
Keywords
generalized entropy optimization methods, stochastic differential equation model, Euler–Maruyama Method, 65C30, 94A17
Citation
İnce, N. & Shamilov, A. (2020). An application of new method to obtain probability density function of solution of stochastic differential equations. Applied Mathematics and Nonlinear Sciences, 5(1), 337–348. https://doi.org/10.2478/amns.2020.1.00031
N. İnce and A. Shamilov, “An application of new method to obtain probability density function of solution of stochastic differential equations,” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 1, pp. 337–348, 2020, doi: 10.2478/amns.2020.1.00031.
İnce N, Shamilov A. An application of new method to obtain probability density function of solution of stochastic differential equations. Applied Mathematics and Nonlinear Sciences. 2020;5(1):337–348. doi:10.2478/amns.2020.1.00031.
İnce, N. and Shamilov, A. (2020), ‘An application of new method to obtain probability density function of solution of stochastic differential equations’, Applied Mathematics and Nonlinear Sciences, 5(1), pp. 337–348. Available at: https://doi.org/10.2478/amns.2020.1.00031.
İnce, Nihal, and Aladdin Shamilov. “An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations.” Applied Mathematics and Nonlinear Sciences, vol. 5, no. 1, 2020, pp. 337–348. https://doi.org/10.2478/amns.2020.1.00031.
İnce, Nihal, and Aladdin Shamilov. “An Application of New Method to Obtain Probability Density Function of Solution of Stochastic Differential Equations.” Applied Mathematics and Nonlinear Sciences 5, no. 1 (2020): 337–348. https://doi.org/10.2478/amns.2020.1.00031.
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Published by: Engineering Journals
