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A generalized entropy optimization modelling in the theory of stochastic differential equations
Ince Nihal 한국통계학회 2022 Journal of the Korean Statistical Society Vol.51 No.2
In this study, we have developed one new approximate method to obtain a probability density function of a solution of a given stochastic diferential equation (SDE) at a fxed time. The mentioned method is based on the estimation SDE ftting 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 fxed 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 diferent 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 fexible distributions. We illustrated the use of this new method to apply the SDE model ftting on S&P 500 stock data.