Introduction to Neutrosophic Stochastic Processes
In this article, the definition of literal neutrosophic stochastic processes is presented for the first time in the form 𝒩𝑡 = 𝜉𝑡 + 𝜂𝑡𝐼 ;𝐼 2 = 𝐼 where both {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜂(𝑡),𝑡 ∈ 𝑇} are classical real valued stochastic processes. Characteristics of the literal neutrosophic stochastic process are...
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| Format: | Article |
| Language: | English |
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University of New Mexico
2023-03-01
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| Series: | Neutrosophic Sets and Systems |
| Subjects: | |
| Online Access: | http://fs.unm.edu/NSS/14IntroNeutroStochasticProcesses.pdf |
| _version_ | 1797824890107068416 |
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| author | Mohamed Bisher Zeina Yasin Karmouta |
| author_facet | Mohamed Bisher Zeina Yasin Karmouta |
| author_sort | Mohamed Bisher Zeina |
| collection | DOAJ |
| description | In this article, the definition of literal neutrosophic stochastic processes is presented for the first time in the form 𝒩𝑡 = 𝜉𝑡 + 𝜂𝑡𝐼 ;𝐼 2 = 𝐼 where both {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜂(𝑡),𝑡 ∈ 𝑇} are classical real valued stochastic processes. Characteristics of the literal neutrosophic stochastic process are defined and its formulas are driven including neutrosophic ensemble mean, neutrosophic covariance function and neutrosophic autocorrelation function. Concept of literal neutrosophic stationary stochastic processes is well defined and many theorems are presented and proved using classical neutrosophic operations then using the one-dimensional AH-Isometry. Some solved examples are presented and solved successfully. We have proved that studying the literal neutrosophic stochastic process {𝒩(𝑡),𝑡 ∈ 𝑇} is equivalent to studying two classical stochastic processes which are {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜉 𝑡 + 𝜂𝑡 ,𝑡 ∈ 𝑇}. |
| first_indexed | 2024-03-13T10:46:00Z |
| format | Article |
| id | doaj.art-1e78b8d7d94245a2bd97396849d9a4c7 |
| institution | Directory Open Access Journal |
| issn | 2331-6055 2331-608X |
| language | English |
| last_indexed | 2024-03-13T10:46:00Z |
| publishDate | 2023-03-01 |
| publisher | University of New Mexico |
| record_format | Article |
| series | Neutrosophic Sets and Systems |
| spelling | doaj.art-1e78b8d7d94245a2bd97396849d9a4c72023-05-17T17:21:44ZengUniversity of New MexicoNeutrosophic Sets and Systems2331-60552331-608X2023-03-015416918310.5281/zenodo.7817748Introduction to Neutrosophic Stochastic ProcessesMohamed Bisher ZeinaYasin KarmoutaIn this article, the definition of literal neutrosophic stochastic processes is presented for the first time in the form 𝒩𝑡 = 𝜉𝑡 + 𝜂𝑡𝐼 ;𝐼 2 = 𝐼 where both {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜂(𝑡),𝑡 ∈ 𝑇} are classical real valued stochastic processes. Characteristics of the literal neutrosophic stochastic process are defined and its formulas are driven including neutrosophic ensemble mean, neutrosophic covariance function and neutrosophic autocorrelation function. Concept of literal neutrosophic stationary stochastic processes is well defined and many theorems are presented and proved using classical neutrosophic operations then using the one-dimensional AH-Isometry. Some solved examples are presented and solved successfully. We have proved that studying the literal neutrosophic stochastic process {𝒩(𝑡),𝑡 ∈ 𝑇} is equivalent to studying two classical stochastic processes which are {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜉 𝑡 + 𝜂𝑡 ,𝑡 ∈ 𝑇}. http://fs.unm.edu/NSS/14IntroNeutroStochasticProcesses.pdfah-isometryneutrosophic field of realsneutrosophic random variablesstationary stochastic processescharacteristics of stochastic processesensemble meancovariance functionautocorrelation function |
| spellingShingle | Mohamed Bisher Zeina Yasin Karmouta Introduction to Neutrosophic Stochastic Processes Neutrosophic Sets and Systems ah-isometry neutrosophic field of reals neutrosophic random variables stationary stochastic processes characteristics of stochastic processes ensemble mean covariance function autocorrelation function |
| title | Introduction to Neutrosophic Stochastic Processes |
| title_full | Introduction to Neutrosophic Stochastic Processes |
| title_fullStr | Introduction to Neutrosophic Stochastic Processes |
| title_full_unstemmed | Introduction to Neutrosophic Stochastic Processes |
| title_short | Introduction to Neutrosophic Stochastic Processes |
| title_sort | introduction to neutrosophic stochastic processes |
| topic | ah-isometry neutrosophic field of reals neutrosophic random variables stationary stochastic processes characteristics of stochastic processes ensemble mean covariance function autocorrelation function |
| url | http://fs.unm.edu/NSS/14IntroNeutroStochasticProcesses.pdf |
| work_keys_str_mv | AT mohamedbisherzeina introductiontoneutrosophicstochasticprocesses AT yasinkarmouta introductiontoneutrosophicstochasticprocesses |