| Title:
|
The narrow recurrence of random dynamical systems (English) |
| Author:
|
Zaou, Ahmed |
| Author:
|
Amouch, Mohamed |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
150 |
| Issue:
|
2 |
| Year:
|
2025 |
| Pages:
|
233-244 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $(\Omega ,\mathcal {F},\mathbb {P})$ be a probability space, where $\mathcal {F}$ is countably generated, and $X$ be a Polish space. Let $\varphi $ be a random dynamical system with time $\mathbb {T}$ on $X$. The skew product flow $ \{\Theta _{t} , \ t\in \mathbb {T} \} $ induced by $\varphi $ is a family of continuous operators acting on $\Pr _{\Omega }(X)$, the set of all probability measures on $X\times \Omega $ with marginal $\mathbb {P}$, which is a Polish space equipped with the narrow topology. In this work, we introduce and study the notion of narrow recurrence of the flow $\{\Theta _{t},\ t\in \mathbb {T} \} $ on ${\rm Pr}_{\Omega }(X)$ and we give some results, which can be considered as an initiation of applications of properties of topological dynamics on stochastic process theory and random dynamical systems. (English) |
| Keyword:
|
hypercyclicity |
| Keyword:
|
transitivity |
| Keyword:
|
recurrence |
| Keyword:
|
the narrow topology |
| Keyword:
|
random dynamical system |
| MSC:
|
37B20 |
| MSC:
|
46E50 |
| MSC:
|
46T25 |
| MSC:
|
47A16 |
| DOI:
|
10.21136/MB.2024.0139-23 |
| . |
| Date available:
|
2025-05-20T11:56:00Z |
| Last updated:
|
2025-05-20 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152973 |
| . |
| Reference:
|
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