Related papers: Sharp moment estimates for polynomial martingales

Estimating extreme quantiles is an important task in many applications, including financial risk management and climatology. More important than estimating the quantile itself is to insure zero coverage error, which implies the quantile…

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the…

We obtain first decay rates of probabilities of tails of multivariate polynomials built on independent random variables with heavy tails. Then we derive stable limit theorems for nonconventional sums of the form $\sum_{Nt\geq n\geq…

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…

Explicit and exact results are obtained for the joint queue-length distribution for the two-level non-preemptive Markovian priority queue. Marginal distributions are derived for the general multi-level problem. The results are based on a…

This work computes the asymptotics of the non-integer moments of the logarithmic derivative of characteristic polynomials of matrices from the $SO(2N+1)$ ensemble. It follows from work of Alvarez and Snaith who computed the asymptotics of…

We study how well moments of sums of independent symmetric random variables with logarithmically concave tails may be approximated by moments of Gaussian random variables.

Consider a strong Markov process in continuous time, taking values in some Polish state space. Recently, Douc, Fort and Guillin (2009) introduced verifiable conditions in terms of a supermartingale property implying an explicit control of…

We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.

We derive in this short report the exponential as well as power decreasing tail estimations for the sums of centered exchangeable random variables, alike ones for the sums of the centered independent ones.

We derive the exact late-time asymptotics for small spherically symmetric solutions of nonlinear wave equations with a potential. The dominant tail is shown to result from the competition between linear and nonlinear effects.

The exact expression for the probability density $p_{_N}(x)$ for sums of a finite number $N$ of random independent terms is obtained. It is shown that the very tail of $p_{_N}(x)$ has a Gaussian form if and only if all the random terms are…

In the paper we study sharp maximal inequalities for martingales and non-negative submartingales: if $f$, $g$ are martingales satisfying \[|\mathrm{d}g_n|\leq|\mathrm{d}f_n|,\qquad n=0,1,2,...,\] almost surely, then…

We establish sharp large-deviation asymptotic estimates for the maximum order statistic of i.i.d.\ standard normal random variables on all Borel subsets of the positive real line. This result yields more accurate tail approximations than…

This paper presents compact notations for concentration inequalities and convenient results to streamline probabilistic analysis. The new expressions describe the typical sizes and tails of random variables, allowing for simple operations…

We investigate the use of optimization to compute bounds for extremal performance measures. This approach takes a non-parametric viewpoint that aims to alleviate the issue of model misspecification possibly encountered by conventional…

In this paper, we will establish a discrete-time version of Clark(-Ocone-Haussmann) formula, which can be seen as an asymptotic expansion in a weak sense. The formula is applied to the estimation of the error caused by the martingale…

Let $X$ be a L\'evy process with absolutely continuous L\'evy measure $\nu$. Small time polynomial expansions of order $n$ in $t$ are obtained for the tails $P(X_{t}\geq{}y)$ of the process, assuming smoothness conditions on the L\'evy…

Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…

We study the exact constants in the moment inequalities for sums of centered independent random variables: improve their asymptotics, low and upper bounds, calculate more exact asymptotics, elaborate the numerical algorithm for their…