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-pro...

Full description

Saved in:
Bibliographic Details
Main Authors: Abdulrahman Astambli, Mohamed Bisher Zeina, Moustafa Mazhar Ranneh
Format: Article
Language:English
Published: University of New Mexico 2025-05-01
Series:Neutrosophic Sets and Systems
Subjects:
Online Access:https://fs.unm.edu/NSS/31PlithogenicStochastic.pdf
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1849224579645440000
author Abdulrahman Astambli
Mohamed Bisher Zeina
Moustafa Mazhar Ranneh
author_facet Abdulrahman Astambli
Mohamed Bisher Zeina
Moustafa Mazhar Ranneh
author_sort Abdulrahman Astambli
collection DOAJ
description 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.
format Article
id doaj-art-a863cfb9886b49d69bcabb98b7802923
institution Kabale University
issn 2331-6055
2331-608X
language English
publishDate 2025-05-01
publisher University of New Mexico
record_format Article
series Neutrosophic Sets and Systems
spelling doaj-art-a863cfb9886b49d69bcabb98b78029232025-08-25T08:00:53ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2025-05-018355356510.5281/zenodo.15171365Introducing Plithogenic Stochastic Processes with an Application to Poisson ProcessAbdulrahman AstambliMohamed Bisher Zeina Moustafa Mazhar RannehIn 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. https://fs.unm.edu/NSS/31PlithogenicStochastic.pdfplithogenic probabilitystochastic processesstationary stochastic processescharacteristics of stochastic processesensemble meancovariance functionautocorrelation functionpoisson process
spellingShingle Abdulrahman Astambli
Mohamed Bisher Zeina
Moustafa Mazhar Ranneh
Introducing Plithogenic Stochastic Processes with an Application to Poisson Process
Neutrosophic Sets and Systems
plithogenic probability
stochastic processes
stationary stochastic processes
characteristics of stochastic processes
ensemble mean
covariance function
autocorrelation function
poisson process
title Introducing Plithogenic Stochastic Processes with an Application to Poisson Process
title_full Introducing Plithogenic Stochastic Processes with an Application to Poisson Process
title_fullStr Introducing Plithogenic Stochastic Processes with an Application to Poisson Process
title_full_unstemmed Introducing Plithogenic Stochastic Processes with an Application to Poisson Process
title_short Introducing Plithogenic Stochastic Processes with an Application to Poisson Process
title_sort introducing plithogenic stochastic processes with an application to poisson process
topic plithogenic probability
stochastic processes
stationary stochastic processes
characteristics of stochastic processes
ensemble mean
covariance function
autocorrelation function
poisson process
url https://fs.unm.edu/NSS/31PlithogenicStochastic.pdf
work_keys_str_mv AT abdulrahmanastambli introducingplithogenicstochasticprocesseswithanapplicationtopoissonprocess
AT mohamedbisherzeina introducingplithogenicstochasticprocesseswithanapplicationtopoissonprocess
AT moustafamazharranneh introducingplithogenicstochasticprocesseswithanapplicationtopoissonprocess