Stable Functional CLT for deterministic systems
| Autor: | Kosloff, Zemer, Volný, Dalibor |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | We show that alpha stable L\'evy motions can be simulated by any ergodic and aperiodic probability preserving transformation. Namely we show: - for $0<\alpha<1$ and every $\alpha$ stable L\'evy motion $\mathbb{W}$, there exists a function f whose partial sum process converges in distribution to $\mathbb{W}$. - for $1\leq \alpha <2$ and every symmetric alpha stable L\'evy motion $\mathbb{W}$, there exists a function f whose partial sum process converges in distribution to $\mathbb{W}$, - for $1< \alpha <2$ and every $-1\leq\beta \leq 1$ there exists a function f whose associated time series is in the classical domain of attraction of an $S_\alpha (\ln(2), \beta,0)$ random variable. Comment: 36 pages |
| Databáze: | arXiv |
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