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Pré-Publication, Document De Travail Année : 2021

CONDITIONED LIMIT THEOREMS FOR HYPERBOLIC DYNAMICAL SYSTEMS

Résumé

Let $(\bb X, T)$ be a subshift of finite type equipped with the Gibbs measure $\nu$ and let $f$ be a real-valued H\"older continuous function on $\bb X$ such that $\nu(f) = 0$. Consider the Birkhoff sums $S_n f = \sum_{k=0}^{n-1} f \circ T^{k}$, $n\geq 1$. For any $t \in \bb R$, denote by $\tau_t^f$ the first time when the sum $t+ S_n f$ leaves the positive half-line for some $n\geq 1$. By analogy with the case of random walks with independent identically distributed increments, we study the asymptotic as $ n\to\infty $ of the probabilities $ \nu(x\in \bb X: \tau_t^f(x)>n) $ and $ \nu(x\in \bb X: \tau_t^f(x)=n) $. We also establish integral and local type limit theorems for the sum $t+ S_n f(x)$ conditioned on the set $\{ x \in \bb X: \tau_t^f(x)>n \}.$
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Dates et versions

hal-03385028 , version 1 (19-10-2021)

Identifiants

  • HAL Id : hal-03385028 , version 1

Citer

Ion Grama, Jean-François Quint, Hui Xiao. CONDITIONED LIMIT THEOREMS FOR HYPERBOLIC DYNAMICAL SYSTEMS. 2021. ⟨hal-03385028⟩
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