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Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is…
We prove a large deviation principle of Freidlin-Wentzell's type for the multivalued stochastic differential equations with monotone drifts, which in particular contains a class of SDEs with reflection in a convex domain.
We give a criterion to determine the large deviation rate functions for abstract dynamical systems on towers. As an application of this criterion we show the level 2 large deviation principle for some class of smooth interval maps with…
In this paper we prove a Large Deviation Principle for the sequence of symmetrised empirical measures $\frac{1}{n} \sum_{i=1}^{n} \delta_{(X^n_i,X^n_{\sigma_n(i)})}$ where $\sigma_n$ is a random permutation and $((X_i^n)_{1 \leq i \leq…
In this paper we investigate the statistics of large waiting times (with respect to the total waiting time) for Bernoulli processes. We determine the corresponding rate functions explicitly and prove a large deviations asymptotic. By this…
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 the symmetric simple exclusion with open boundaries that are in contact with particle reservoirs at different densities. The reservoir densities changes at a slower time scale with respect to the natural time scale the system…
We extend the study by Ornstein and Weiss on the asymptotic behavior of the normalized version of recurrence times and establish the large deviation property for a certain class of mixing processes. Further, an estimator for entropy based…
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…
We consider probability measures on $A^N$, the set of sequences of symbols on a finite alphabet $A$ of length $N$, that give a weight to each sequence in terms of a collection of matrices with non-negative entries and having rows and…
We establish a Large Deviations Principle for stochastic processes with Lipschitz continuous oblique reflections on regular domains. The rate functional is given as the value function of a control problem and is proved to be good. The proof…
We investigate large deviations for the empirical measure of the position and momentum of a particle traveling in a box with hot walls. The particle travels with uniform speed from left to right, until it hits the right boundary. Then it is…
In this paper we prove the continuity of all Lyapunov exponents, as well as the continuity of the Oseledets decomposition, for a class of irreducible cocycles over strongly mixing Markov shifts. Moreover, gaps in the Lyapunov spectrum lead…
We obtain large deviations for a class of dependent random variables in the domain of attraction of an $\alpha$-stable law, $\alpha\in (0, 1)\cup (1, 2]$. This class includes ergodic sums of observables in the domain of attraction of an…
This work concerns generalized backward stochastic differential equations, which are coupled with a family of reflecting diffusion processes. First of all, we establish the large deviation principle for forward stochastic differential…
This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…
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…
Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele…
Let $\sigma(u)$, $u\in \mathbb{R}$ be an ergodic stationary Markov chain, taking a finite number of values $a_1,...,a_m$, and $b(u)=g(\sigma(u))$, where $g$ is a bounded and measurable function. We consider the diffusion type process $$…
We investigate the Large Deviation behavior in small time of continuous Gaussian processes. We introduce a general procedure allowing to derive Large Deviation Principles in small time starting from the well understood context of Large…