Related papers: Large Deviation Principles via Spherical Integrals

For Markov processes evolving on multiple time-scales a combination of large component scalings and averaging of rapid fluctuations can lead to useful limits for model approximation. A general approach to proving a law of large numbers to a…

In this paper, we are concerned with multi-scale distribution dependent stochastic differential equations driven by fractional Brownian motion (with Hurst index $H>\frac12$ and standard Brownian motion, simultaneously. Our aim is to…

The aim of this paper is to improve the large deviation principle for the number of descents in a random permutation by establishing a sharp large deviation principle of any order. We shall also prove a sharp large deviation principle of…

In this short note we consider semi-Markov processes satisfying the condition of direction-time independence (Markov renewal processes). We derive large deviation principles and fluctuation theorems for the empirical current and the…

Consider the stochastic differential equation in $\rr^d$ dX^{\e}_t&=b(X^{\e}_t)dt+\sqrt{\e}\sigma(X^\e_t)dB_t X^{\e}_0&=x_0,\quad x_0\in\rr^d$ where $b:\rr^d\to\rr^d$ is $C^1$ such that $<x,b(x)> \leq C(1+|x|^2)$, $\sigma:\rr^d\to…

We derive a large deviation principle for families of random variables in the basin of attraction of spectrally positive stable distributions by proving a uniform version of the Tauberian theorem for Laplace-Stieltjes transforms. The main…

We prove an large deviation principle for multivalued sdes

In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…

In this article we establish a large deviation principle for the family {\nu_{\epsilon}:\epsilon \in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrt{\epsilon}}Z_t}_{t\leq 1}, where (Z_t)_{t\in \lbrack 0,1]} is a…

In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…

We describe large deviations for normalized multiple iterated sums and integrals of the form $\bbS_N^{(\nu)}(t)=N^{-\nu}\sum_{0\leq k_1<...<k_\nu\leq Nt}\xi(k_1)\otimes\cdots\otimes\xi(k_\nu)$, $t\in[0,T]$ and…

We prove large and moderate deviation principles for the distribution of an empirical mean conditioned by the value of the sum of discrete i.i.d. random variables. Some applications for combinatoric problems are discussed.

We establish the large deviation principle for a topological Markov shift over infinite alphabet which satisfies strong combinatorial assumptions called ``finite irreducibility'' or ``finite primitiveness''. More precisely, we assume the…

We establish precise upper-tail asymptotics and large deviation principles for the rightmost eigenvalue $\lambda_1$ of Wigner matrices with sub-Gaussian entries. In contrast to the case of heavier tails, where deviations of $\lambda_1$ are…

We study the large deviations principle for one dimensional, continuous, homogeneous, strong Markov processes that do not necessarily behave locally as a Wiener process. Any strong Markov process $X_{t}$ in $\mathbb{R}$ that is continuous…

This paper is concerned with the general theme of relating the Large Deviation Principle (LDP) for the invariant measures of stochastic processes to the associated sample path LDP. It is shown that if the sample path deviation function…

Let $U_m$ be an $m \times m$ Haar unitary matrix and $U_{[m,n]}$ be its $n \times n$ truncation. In this paper the large deviation is proven for the empirical eigenvalue density of $U_{[m,n]}$ as $m/n \to \lambda $ and $n \to \infty$. The…

We consider a finite collection of independent Hermitian heavy-tailed random matrices of growing dimension. Our model includes the L\'evy matrices proposed by Bouchaud and Cizeau, as well as sparse random matrices with O(1) non-zero entries…

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 deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…