Weak convergence to extremal processes and record events for non-uniformly hyperbolic dynamical systems
| Autor: | Mike Todd, Mark Holland |
|---|---|
| Přispěvatelé: | University of St Andrews. Pure Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Scheme (programming language)
Weak convergence Dynamical systems theory business.industry Applied Mathematics General Mathematics 010102 general mathematics T-NDAS Dynamical Systems (math.DS) 01 natural sciences Work (electrical) Hospitality 0103 physical sciences FOS: Mathematics 010307 mathematical physics QA Mathematics 0101 mathematics Mathematics - Dynamical Systems business QA computer Mathematical economics computer.programming_language Mathematics |
| Popis: | For a measure preserving dynamical system $(\mathcal{X},f, \mu)$, we consider the time series of maxima $M_n=\max\{X_1,\ldots,X_n\}$ associated to the process $X_n=\phi(f^{n-1}(x))$ generated by the dynamical system for some observable $\phi:\mathcal{X}\to\mathbb{R}$. Using a point process approach we establish weak convergence of the process $Y_n(t)=a_n(M_{[nt]}-b_n)$ to an extremal process $Y(t)$ for suitable scaling constants $a_n,b_n\in\mathbb{R}$. Convergence here taking place in the Skorokhod space $\mathbb{D}(0,\infty)$ with the $J_1$ topology. We also establish distributional results for the record times and record values of the corresponding maxima process. Comment: To appear in Ergodic Theory Dynam. Systems |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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