Related papers: A generalization of Cram\'{e}r large deviations fo…

We propose three new discrete variational schemes that capture the conservative-dissipative structure of a generalized Kramers equation. The first two schemes are single-step minimization schemes while the third one combines a streaming and…

The essentials of fractional calculus according to different approaches that can be useful for our applications in the theory of probability and stochastic processes are established. In addition to this, from this fractional integral one…

While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…

Borgs, Chayes, Gaudio, Petti and Sen [arXiv:2007.14508] proved a large deviation principle for block model random graphs with rational block ratios. We strengthen their result by allowing any block ratios (and also establish a simpler…

In many epidemiological contexts, disease occurrences and their rates are naturally modelled by counting processes and their intensities, allowing an analysis based on martingale methods. These methods lend themselves to extensions of…

We prove large deviations principles for spectral measures of perturbed (or spiked) matrix models in the direction of an eigenvector of the perturbation. In each model under study, we provide two approaches, one of which relying on large…

We present an efficient finite difference method for the computation of parameter sensitivities that is applicable to a wide class of continuous time Markov chain models. The estimator for the method is constructed by coupling the perturbed…

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as…

Using a variational technique, we generalize the statistical physics approach of learning from random examples to make it applicable to real data. We demonstrate the validity and relevance of our method by computing approximate estimators…

We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…

In this paper we show a some new look at large deviation theorems from the viewpoint of the information-spectrum (IS) methods, which has been first exploited in information theory, and also demonstrate a new basic formula for the large…

This paper is devoted to the problem of sample path large deviations for the Markov processes on R_+^N having a constant but different transition mechanism on each boundary set {x:x_i=0 for i\notin\Lambda, x_i>0 for i\in\Lambda}. The global…

We provide a direct proof of Cram\'er's theorem for geodesic random walks in a complete Riemannian manifold $(M,g)$. We show how to exploit the vector space structure of the tangent spaces to study large deviation properties of geodesic…

Generalized additive models (GAMs) are a widely used class of models of interest to statisticians as they provide a flexible way to design interpretable models of data beyond linear models. We here propose a scalable and well-calibrated…

We consider the probability that a weighted sum of $n$ i.i.d. random variables $X_j$, $j = 1, . . ., n$, with stretched exponential tails is larger than its expectation and determine the rate of its decay, under suitable conditions on the…

We develop a general framework for extracting highly uniform bounds on local stability for stochastic processes in terms of information on fluctuations or crossings. This includes a large class of martingales: As a corollary of our main…

In this paper, we establish normalized and self-normalized Cram\'er-type moderate deviations for Euler-Maruyama scheme for SDE. As a consequence of our results, Berry-Esseen's bounds and moderate deviation principles are also obtained. Our…

Fluctuations in small biological systems can be crucial for their function. Large-deviation theory characterizes such rare events from the perspective of stochastic processes. In most cases it is very difficult to directly determine the…

In this paper we study the exponential twist, i.e. a path-integral exponential change of measure, of a Markovian reference probability measure $\P$. This type of transformation naturally appears in variational representation formulae…

We derive a large deviation principle for random permutations induced by probability measures of the unit square, called permutons. These permutations are called $\mu$-random permutations. We also introduce and study a new general class of…