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

In this paper we deal with the generalized Gamma processes and their compositions. For the compositions of two or more than two generalized Gamma processes we give, when possible, the explicit law whereas, in the other cases the…

We derive a large deviation principle for the empirical currents of lattice gas dynamics which combine a fast stirring mechanism (Symmetric Simple Exclusion Process) and creation/annihilation mechanisms (Glauber dynamics). Previous results…

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…

The survey is dedicated to a celebrated series of quantitave results, developed by the Lithuanian school of probability, on the normal approximation for a real-valued random variable. The key ingredient is a bound on cumulants of the type…

Rare trajectories of stochastic systems are important to understand -- because of their potential impact. However, their properties are by definition difficult to sample directly. Population dynamics provides a numerical tool allowing their…

We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…

We consider (annealed) large deviation principles for component empirical measures of several families of marked sparse random graphs, including (i) uniform graphs on $n$ vertices with a fixed degree distribution; (ii) uniform graphs on $n$…

Divergence functions are measures of distance or dissimilarity between probability distributions that serve various purposes in statistics and applications. We propose decompositions of Wasserstein and Cram\'er distances$-$which compare two…

We use the martingale convergence method to get the weak convergence theorem on general functionals of partial sums of independent heavy-tailed random variables. The limiting process is the stochastic integral driven by $\alpha-$stable…

We study using large deviation theory the fluctuations of time-integrated functionals or observables of the unbiased random walk evolving on Erd\"os-R\'enyi random graphs, and construct a modified, biased random walk that explains how these…

In this paper, we study the self-normalized Cram\a'{e}r-type moderate deviations for centered independent random variables $X_1, X_2,...$ with $0<E |X_i|^3 <\infty$. The main results refine Theorems 1.1 and 1.2 of Wang (2011), the…

Dzhaparidze and Spreij [5] showed that the quadratic variation of a semimartingale can be approximated using a randomized periodogram. We show that the same approximation is valid for a special class of continuous stochastic processes. This…

Let $(Z_n)$ be a supercritical branching process in a random environment $\xi = (\xi_n)$. We establish a Berry-Esseen bound and a Cram\'er's type large deviation expansion for $\log Z_n$ under the annealed law $\mathbb P$. We also improve…

The purpose of this paper is to ensure the conditions of G\"artner-Ellis Theorem for evaluations of the empirical measure. We show that up-to-date conditions for ensuring the convergence to a quasi-stationary distribution can be applied…

The large deviations at 'Level 2.5 in time' for time-dependent ensemble-empirical-observables, introduced by C. Maes, K. Netocny and B. Wynants [Markov Proc. Rel. Fields. 14, 445 (2008)] for the case of $N$ independent Markov jump…

We derive a discrete version of the stochastic Gronwall Lemma found in [Scheutzow, IDAQP, 2013]. The proof is based on a corresponding deterministic version of the discrete Gronwall Lemma and an inequality bounding the supremum in terms of…

We consider a fractional generalization of Hamiltonian and gradient systems. We use differential forms and exterior derivatives of fractional orders. We derive fractional generalization of Helmholtz conditions for phase space. Examples of…

In this article, we first establish derivative formulae for fractional Gruschin type process, which generalize the result of Wang (J Theor Probab 27:80--95, Theorem 1.1, 2012). Since we work on a non-Markovian context, some technical…

Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential…

Recent advances in stochastic gradient variational inference have made it possible to perform variational Bayesian inference with posterior approximations containing auxiliary random variables. This enables us to explore a new synthesis of…