# Conditioned limit theorems for hyperbolic dynamical systems

@inproceedings{Grama2021ConditionedLT, title={Conditioned limit theorems for hyperbolic dynamical systems}, author={Ion Grama and Jean-François Quint and Hui Xiao}, year={2021} }

Let (X, T ) be a subshift of finite type equipped with the Gibbs measure ν and let f be a real-valued Hölder continuous function on X such that ν(f) = 0. Consider the Birkhoff sums Snf = ∑n−1 k=0 f ◦ T , n > 1. For any t ∈ R, denote by τ t the first time when the sum t + Snf leaves the positive half-line for some n > 1. By analogy with the case of random walks with independent identically distributed increments, we study the asymptotic as n → ∞ of the probabilities ν(x ∈ X : τ t (x) > n) and…

## One Citation

Conditioned local limit theorems for random walks on the real line

- Mathematics
- 2021

Abstract. Consider a random walk Sn = ∑n i=1 Xi with independent and identically distributed real-valued increments Xi of zero mean and finite variance. Assume that Xi is non-lattice and has a moment…

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