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...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2025-05-01
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| Series: | Neutrosophic Sets and Systems |
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| Online Access: | https://fs.unm.edu/NSS/31PlithogenicStochastic.pdf |
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| 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 |