Generalized entropy optimization methods in stochastic differential equation modeling

In order for stochastic differential equations to be applied to a problem, it is quite important that its solution can be proved that it exists and is the only one. For this purpose, the solution of stochastic differential equations, which is different from the literature, exists and is the only one, has been theoretically proved in this thesis study with the help of the generalization of the Banach fixed point principle. The solution of stochastic differential equations is a stochastic process, and this process represents a random variable at each time of t time. It is an important problem that these random variables forming the stochastic process are the possibility density function. In this study, the solution of the problem in question is, a new method for obtaining the probability density function of the stochastic process, which is the solution of stochastic differential equations using generalized entropy optimization methods, has been developed and also theoretically proved. The reason for using generalized entropy optimization methods is that these methods are derived from this is because distributions are more flexible than other statistical distributions. In order to demonstrate the performance of the new method developed, its application was carried out on three real data sets and the results obtained by the simulation study were supported.