• Corpus ID: 239024592

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… 
Conditioned local limit theorems for random walks on the real line
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

References

SHOWING 1-10 OF 32 REFERENCES
Conditioned local limit theorems for random walks on the real line
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
Limit theorems for Markov walks conditioned to stay positive under a spectral gap assumption
Consider a Markov chain (X n) n0 with values in the state space X. Let f be a real function on X and set S 0 = 0, S n = f (X 1) + · · · + f (X n), n 1. Let P x be the probability measure generated by
A local limit theorem for random walks conditioned to stay positive
We consider a real random walk Sn=X1+...+Xn attracted (without centering) to the normal law: this means that for a suitable norming sequence an we have the weak convergence Sn/an⇒ϕ(x)dx, ϕ(x) being
On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive
Let {Xk : k ≧ 1} be a sequence of i.i.d.rv with E(Xi) = 0 and E(X2 i ) = σ2, 0 < σ2 < ∞. Set Sn = X1 + · · · + Xn. Let Yn(t) be Sk/σn 1 2 for t = k/n and suitably interpolated elsewhere. This paper
Local behaviour of first passage probabilities
Suppose that S is an asymptotically stable random walk with norming sequence cn and that Tx is the time that S first enters (x, ∞), where x ≥ 0. The asymptotic behaviour of P(T0 = n) has been
Limit Theorems for Markov Chains and Stochastic Properties of Dynamical Systems by Quasi-Compactness
General Facts About The Method Purpose Of The Paper.- The Central Limit Theorems For Markov Chains Theorems A, B, C.- Quasi-Compact Operators of Diagonal Type And Their Perturbations.- First
The central limit theorem for geodesic flows onn-dimensional manifolds of negative curvature
AbstractIn this paper we prove a central limit theorem for special flows built over shifts which satisfy a uniform mixing of type $$\gamma ^{n^\alpha } $$ , 00. The function defining the special flow
On conditioning a random walk to stay nonnegative
Let S be a real-valued random walk that does not drift to ∞, so P(S k ≥ 0 for all k)=0. We condition S to exceed n before hitting the negative halfline, respectively, to stay nonnegative up to time
Random walks in cones
We study the asymptotic behavior of a multidimensional random walk in a general cone. We find the tail asymptotics for the exit time and prove integral and local limit theorems for a random walk
An exact rate of convergence in the functional central limit theorem for special martingale difference arrays
SummarySince the topology of weak convergence of probability distributions on the Borel σ-field of the space C= C([0, 1]) is metrizable, it is natural to describe the speed of convergence in weak
...
1
2
3
4
...