Related papers: Large deviations for dynamical systems with stretc…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
In this paper we establish a large deviations type estimate for strongly mixing Markov chains with respect to the Lp norm. As applications we derive such estimates for the iterates of a locally constant random cocycle with mixed rank, as…
We consider exponential large deviations estimates for unbounded observables on uniformly expanding dynamical systems. We show that uniform expansion does not imply the existence of a rate function for unbounded observables no matter the…
We estimate the speed of decay of correlations for general nonuniformly expanding dynamical systems, using estimates on the time the system takes to become really expanding. Our method can deal with fast decays, such as exponential or…
Large deviations in chaotic dynamics have potentially significant and dramatic consequences. We study large deviations of series of finite lengths $N$ generated by chaotic maps. The distributions generally display an exponential decay with…
We obtain estimates on the decay of correlations, Central Limit Theorem and Large Deviations for dynamical systems admitting an induced weak Gibbs--Markov map, for larger classes of observables with weaker regularity than H\"{o}lder,…
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…
The large deviations of an infinite moving average process with exponentially light tails are very similar to those of an i.i.d. sequence as long as the coefficients decay fast enough. If they do not, the large deviations change…
The large deviations principles are established for a class of multidimensional degenerate stochastic differential equations with reflecting boundary conditions. The results include two cases where the initial conditions are adapted and…
We consider low--dimensional dynamical systems with a mixed phase space and discuss the typical appearance of slow, polynomial decay of correlations: in particular we emphasize how this mixing rate is related to large deviations properties.
We propose a method to calculate the large deviations of current fluctuations in a class of stochastic particle systems with history-dependent rates. Long-range temporal correlations are seen to alter the speed of the large deviation…
In Pires {\it et al.} [Phys. Rev. E 84, 066210 (2011)] intermittent maps are considered, and the tight relationship between correlation decay of smooth observables and large deviations estimates, as for instance employed in Artuso and…
We develop a martingale approximation framework yielding quantitative maximal large deviations estimates for invertible dynamical systems. From suitable decay of correlations, we deduce these estimates and, as an application, we obtain…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
We estimate density and regression functions for weak dependant datas. Using an exponential inequality obtained by Dedecker and Prieur and in a previous article of the author, we control the deviation between the estimator and the function…
We consider the maximum entropy Markov chain inference approach to characterize the collective statistics of neuronal spike trains, focusing on the statistical properties of the inferred model. We review large deviations techniques useful…
We introduce and test an algorithm that adaptively estimates large deviation functions characterizing the fluctuations of additive functionals of Markov processes in the long-time limit. These functions play an important role for predicting…
One-dimensional run-and-tumble processes may converge towards some localized non-equilibrium steady state when the two velocities and/or the two switching rates are space-dependent. A long dynamical trajectory can be then analyzed via the…
The theory of large deviations is concerned with the exponential decay of probabilities of large fluctuations in random systems. These probabilities are important in many fields of study, including statistics, finance, and engineering, as…
We claim that looking at probability distributions of \emph{finite time} largest Lyapunov exponents, and more precisely studying their large deviation properties, yields an extremely powerful technique to get quantitative estimates of…