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Markov Characteristics for IFSP and IIFSP | ||
| Transactions on Fuzzy Sets and Systems | ||
| مقاله 9، دوره 1، شماره 2، بهمن 2022، صفحه 72-89 اصل مقاله (269.14 K) | ||
| نوع مقاله: Original Article | ||
| شناسه دیجیتال (DOI): 10.30495/tfss.2022.1961482.1039 | ||
| نویسندگان | ||
| Nan Jiang* 1؛ Wei Li2؛ Fei Li1؛ Juntao Wang1 | ||
| 1School of Science Xi'an Shiyou University Xi'an, China | ||
| 2Institute for Advanced Studies in The History of Science Northwest University Xi'an, China | ||
| چکیده | ||
| 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. | ||
| کلیدواژه‌ها | ||
| Fractal؛ Markov process؛ Iterated function system؛ Probability | ||
| مراجع | ||
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