Investigating stochastic differential models based on the statistical point of view and its applications

Authors
Mehdi Shams 1
Gholamreza Hesamian 2
1 University of Kashan
2 Payame Noor University
Abstract
In this paper, the probability density function of the process, its trend functions, the maximum likelihood estimate and the confidence interval of the parameters are calculated. This paper investigates a nonhomogeneous state of a diffusion process with a time-dependent velocity reduction coefficient. First, the process probability density function and trend functions are calculated and then, using discrete sampling, statistical inferences such as estimating the parameters by the maximum likelihood method, finding the distribution of the obtained estimators and the confidence interval of the parameters are performed. Finally, for the simulated data, the applications of this model are introduced.



In this paper, from the point of view of statistical inference, stochastic differential equation models are studied. A heterogeneous case of a diffusion process with time-dependent deceleration coefficient and stochastic differential equation models with random effects are investigated and an approximation for the nonlinear stochastic differential equation is presented. Also, with the help of time series analysis and statistical methods, the parameters of stochastic differential equation models are estimated.At the end, the application of invariant copulas in the modeling of stochastic differential equations is expressed. In each of these cases, the process probability density function and trend functions are calculated, and statistical inferences such as point estimation, interval estimation, selection of the best model, and numerical analyzes and simulations are performed in stochastic differential equations.


Keywords
Wiener process
Stochastic Differential Equations
Maximum Likelihood estimation
Akaike information criterion
Parameter estimation
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