Markov Characteristics for IFSP and IIFSP
As the research object of modern nonlinear science, a fractal theory has been an important research content for scholars since it comes into the world. Moreover, iterated function system (IFS) is a significant research object of fractal theory. On the other hand, the Markov process plays...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Islamic Azad University, Bandar Abbas Branch
2022-11-01
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| Series: | Transactions on Fuzzy Sets and Systems |
| Subjects: | |
| Online Access: | https://tfss.journals.iau.ir/article_692670_1fd135261135829c9ebe426f6cd201b7.pdf |
| _version_ | 1797827948836814848 |
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| author | Nan Jiang Wei Li Fei Li Juntao Wang |
| author_facet | Nan Jiang Wei Li Fei Li Juntao Wang |
| author_sort | Nan Jiang |
| collection | DOAJ |
| description | As the research object of modern nonlinear science, a fractal theory has been an important research content for scholars since it comes into the world. Moreover, iterated function system (IFS) is a significant research object of fractal theory. On the other hand, the Markov process plays an important role in the stochastic process. In this paper, the iterated function system with probability(IFSP) and the infinite function system with probability(IIFSP) are investigated by using interlink, period, recurrence and some related concepts. Then, some important properties are obtained, such as: 1. The sequence of stochastic variable $\{\zeta_{n},(n\geq 0)\}$ is a homogenous Markov chain. 2. The sequence of stochastic variable $\{\zeta_{n},(n\geq 0)\}$ is an irreducible ergodic chain. 3. The distribution of transition probability $ p_{ij}^{(n)}$ based on $n\rightarrow\infty $ is a stationary probability distribution. 4. The state space can be decomposed of the union of the finite(or countable) mutually disjoint subsets, which are composed of non-recurrence states and recurrence states respectively. |
| first_indexed | 2024-04-09T12:56:36Z |
| format | Article |
| id | doaj.art-f549b43e1e87424297d18721da2cf47d |
| institution | Directory Open Access Journal |
| issn | 2821-0131 |
| language | English |
| last_indexed | 2024-04-09T12:56:36Z |
| publishDate | 2022-11-01 |
| publisher | Islamic Azad University, Bandar Abbas Branch |
| record_format | Article |
| series | Transactions on Fuzzy Sets and Systems |
| spelling | doaj.art-f549b43e1e87424297d18721da2cf47d2023-05-13T17:27:53ZengIslamic Azad University, Bandar Abbas BranchTransactions on Fuzzy Sets and Systems2821-01312022-11-0112728910.30495/tfss.2022.1961482.1039692670Markov Characteristics for IFSP and IIFSPNan Jiang0Wei Li1Fei Li2Juntao Wang3School of Science Xi'an Shiyou University Xi'an, ChinaInstitute for Advanced Studies in The History of Science Northwest University Xi'an, ChinaSchool of Science Xi'an Shiyou University Xi'an, ChinaSchool of Science Xi'an Shiyou University Xi'an, ChinaAs the research object of modern nonlinear science, a fractal theory has been an important research content for scholars since it comes into the world. Moreover, iterated function system (IFS) is a significant research object of fractal theory. On the other hand, the Markov process plays an important role in the stochastic process. In this paper, the iterated function system with probability(IFSP) and the infinite function system with probability(IIFSP) are investigated by using interlink, period, recurrence and some related concepts. Then, some important properties are obtained, such as: 1. The sequence of stochastic variable $\{\zeta_{n},(n\geq 0)\}$ is a homogenous Markov chain. 2. The sequence of stochastic variable $\{\zeta_{n},(n\geq 0)\}$ is an irreducible ergodic chain. 3. The distribution of transition probability $ p_{ij}^{(n)}$ based on $n\rightarrow\infty $ is a stationary probability distribution. 4. The state space can be decomposed of the union of the finite(or countable) mutually disjoint subsets, which are composed of non-recurrence states and recurrence states respectively.https://tfss.journals.iau.ir/article_692670_1fd135261135829c9ebe426f6cd201b7.pdffractalmarkov processiterated function systemprobability |
| spellingShingle | Nan Jiang Wei Li Fei Li Juntao Wang Markov Characteristics for IFSP and IIFSP Transactions on Fuzzy Sets and Systems fractal markov process iterated function system probability |
| title | Markov Characteristics for IFSP and IIFSP |
| title_full | Markov Characteristics for IFSP and IIFSP |
| title_fullStr | Markov Characteristics for IFSP and IIFSP |
| title_full_unstemmed | Markov Characteristics for IFSP and IIFSP |
| title_short | Markov Characteristics for IFSP and IIFSP |
| title_sort | markov characteristics for ifsp and iifsp |
| topic | fractal markov process iterated function system probability |
| url | https://tfss.journals.iau.ir/article_692670_1fd135261135829c9ebe426f6cd201b7.pdf |
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