Introducing Plithogenic Stochastic Processes with an Application to Poisson Process

In this paper, we study and define the mathematical form of plithogenic stochastic processes PSP based on set of three classic stochastic processes. This new definition is a generalization of neutrosophic stochastic process. characteristics of PSP are defined and theorems related to it were well-proved. Also, definition of weakly stationary PSP is introduced and it is proved that a plithogenic stochastic process is weakly stationary if and only if three corresponding crisp stochastic processes are weakly stationary. We also prove that the autocorrelation function of a plithogenic stochastic process is an even bounded function. As an application of this new form of stochastic processes, plithogenic Poisson process is defined and its properties are discussed. Solved example related to plithogenic Poisson process is successfully presented and solved. This new type of stochastic processes opens the road to many future researches in stochastic modelling.