Related papers: A transfer principle for deviations principles
The aim of this paper is to prove an uncertainty principle for the representation of a vector in two bases. Our result extends previously known qualitative uncertainty principles into quantitative estimates. We then show how to transfer…
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…
We present precise moderate deviation probabilities, in both quenched and annealed settings, for a recurrent diffusion process with a Brownian potential. Our method relies on fine tools in stochastic calculus, including Kotani's lemma and…
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to…
We establish an abstract, effective, exponential large deviations type estimate for Markov systems satisfying a weaker form of mixing. We employ this result to derive such estimates, as well as a central limit theorem, for the skew product…
A moderate deviation principle for nonlinear functions of Gaussian processes is established. The nonlinear functions need not be locally bounded. Especially, the logarithm is allowed. (Thus, small deviations of the process are relevant.)…
We consider systems of slow--fast diffusions with small noise in the slow component. We construct provably logarithmic asymptotically optimal importance schemes for the estimation of rare events based on the moderate deviations principle.…
A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions.…
In this paper, using Zvonkin type transform, the large deviation principle is proved for stochastic differential equations with Dini continuous drifts, where the existed methods for large deviation principle are unavailable. The method and…
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…
In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from…
A variational formula for the asymptotic variance of general Markov processes is obtained. As application, we get a upper bound of the mean exit time of reversible Markov processes, and some comparison theorems between the reversible and…
The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for…
In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.
The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It\^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result…
We provide the large deviation principle for higher dimensional piecewise expanding maps and by using the functional approach of Hennion and Herv\'e, slightly modified.
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
A method for designing variational principles for the dynamics of a possibly dissipative and non-conservatively forced chain of particles is demonstrated. Some qualitative features of the formulation are discussed.
We prove a large deviations principle for the empirical law of the block sizes of a uniformly distributed non-crossing partition. As an application we obtain a variational formula for the maximum of the support of a compactly supported…
A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by using noncommutative determinants. These properties enable us…