A generalized entropy optimization modelling in the theory of stochastic differential equations

Autor: Nihal Ince
Rok vydání: 2021
Předmět:
Zdroj: Journal of the Korean Statistical Society. 51:337-355
ISSN: 2005-2863
1226-3192
DOI: 10.1007/s42952-021-00139-z
Popis: In this study, we have developed one new approximate method to obtain a probability density function of a solution of a given stochastic differential equation (SDE) at a fixed time. The mentioned method is based on the estimation SDE fitting to given statistical data and approximate methods solving SDE. For this purpose, by approximate methods solving SDE trajectories of this equation are constructed. For example, it is possible to use the Euler–Maruyama (EM) method. By using trajectories at a fixed time are obtained reasonable random variables of the solution of SDE. The probability density function of the mentioned random variables is obtained. It is possible to use different statistical methods. These results are acquired by using the theorem. In our investigation, it is used Generalized Entropy Optimization Methods (GEOM). The reason using GEOM’s is explained oneself by the fact that these methods represent distributions that are more flexible distributions. We illustrated the use of this new method to apply the SDE model fitting on S&P 500 stock data.
Databáze: OpenAIRE
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