Introducing Plithogenic Stochastic Processes with an  Application to Poisson Process

Abdulrahman Astambli; Mohamed Bisher Zeina; Moustafa Mazhar Ranneh

Authors

Abdulrahman Astambli Faculty of Science, Dept. of Mathematical Statistics, University of Aleppo, Aleppo, Syria
Mohamed Bisher Zeina Faculty of Science, Dept. of Mathematical Statistics, University of Aleppo, Aleppo, Syria
Moustafa Mazhar Ranneh Faculty of Science, Dept. of Mathematical Statistics, University of Aleppo, Aleppo, Syria

Keywords:

Plithogenic Probability, Stochastic Processes, Stationary Stochastic Processes, Characteristics of Stochastic Processes, Ensemble Mean, Covariance Function, Autocorrelation Function, Poisson Process.

Abstract

: 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.

DOI: 10.5281/zenodo.15171365