Related papers: Hitting time statistics for observations of dynami…
We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…
We consider expanding systems with invariant measures that are uniformly expanding everywhere except on a small measure set and show that the limiting statistics of hitting times for zero measure sets are compound Poisson provided the…
We continue our study of exponential law for occurrences and returns of patterns in the context of Gibbsian random fields. For the low temperature plus phase of the Ising model, we prove exponential laws with error bounds for occurrence,…
We cosider random dynamical systems with randomly chosen jumps. The choice of deterministic dynamical system and jumps depends on a position. We proove the existence of an exponentially attractive invariant measure and the strong law of…
We prove that for any $\alpha$-mixing stationnary process the hitting time of any $n$-string $A_n$ converges, when suitably normalized, to an exponential law. We identify the normalization constant $\lambda(A_n)$. A similar statement holds…
This paper presents an analysis of the distribution of the time $\tau$ between two consecutive events in a stationary point process. The study is motivated by the discovery of a unified scaling law for $\tau$ for the case of seismic events.…
This paper discusses the evolution of probability distributions for certain time-dependent dynamical systems. Exponential loss of memory is proved for expanding maps and for one-dimensional piecewise expanding maps with slowly varying…
Hysteresis loops and the associated avalanche statistics of spin systems, such as the random-field Ising and Edwards-Anderson spin-glass models, have been extensively studied. A particular focus has been on self-organized criticality,…
We investigate the convergence of hitting times for jump-diffusion processes. Specifically, we study a sequence of stochastic differential equations with jumps. Under reasonable assumptions, we establish the convergence of solutions to the…
Random metastability occurs when an externally forced or noisy system possesses more than one state of apparent equilibrium. This work investigates fluctuations in a class of random dynamical systems, arising from randomly perturbing a…
We consider the distribution of the duration time, the time elapsed since it began, of a diffusion process given its present position, under the assumption that the process began at the origin. For unbiased diffusion, the distribution does…
We prove an explicit formula of hitting times in terms of enumerations of spanning trees for random walks on general connected graphs. We apply the formula to improve Lawler's bound of hitting times for general graphs, prove a sharp bound…
We study the statistical distribution of the closest encounter between generic smooth observations computed along different trajectories of a rapidly mixing dynamical system. At the limit of large trajectories, we obtain a distribution of…
An analytical study of the return time distribution of extreme events for stochastic processes with power-law correlation has been carried on. The calculation is based on an epsilon-expansion in the correlation exponent:…
The recurrence times between extreme events have been the central point of statistical analyses in many different areas of science. Simultaneously, the Poincar\'e recurrence time has been extensively used to characterize nonlinear dynamical…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
This paper introduces a novel approach to investigate the dynamics of state distributions, which accommodate both cross-sectional distributions of repeated panels and intra-period distributions of a time series observed at high frequency.…
In the setting of non-reversible Markov chains on finite or countable state space, exact results on the distribution of the first hitting time to a given set $G$ are obtained. A new notion of "strong metastability time" is introduced to…
Hitting times provide a fundamental measure of distance in random processes, quantifying the expected number of steps for a random walk starting at node $u$ to reach node $v$. They have broad applications across domains such as network…
In this paper, we focus on the hitting times of a stochastic epidemic model presented by \cite{Gray}. Under the help of the auxiliary stopping times, we investigate the asymptotic limits of the hitting times by the variations of calculus…