Related papers: A supermartingale argument for characterizing the …
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
It has been shown that sufficiently well mixing dynamical systems with positive entropy have extreme value laws which in the limit converge to one of the three standard distributions known for i.i.d. processes, namely Gumbel, Fr\'echet and…
We study the short-time asymptotics of conditional expectations of smooth and non-smooth functions of a (discontinuous) Ito semimartingale; we compute the leading term in the asymptotics in terms of the local characteristics of the…
This paper provides a detailed description for the asymptotics of exponential functionals of random walks with light/heavy tails. We give the convergence rate based on the key observation that the asymptotics depends on the sample paths…
We derive the joint asymptotic distribution of empirical quantiles and expected shortfalls under general conditions on the distribution of the underlying observations. In particular, we do not assume that the distribution function is…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
We prove a law of large numbers and functional central limit theorem for a class of multivariate Hawkes processes with time-dependent reproduction rate. We address the difficulties induced by the use of non-convolutive Volterra processes by…
This article is a survey of the results on asymptotic behavior of small ball probabilities in $L_2$-norm. Recent progress in this field is mainly based on the methods of spectral theory of differential and integral operators.
We show in this paper that many risk measures arising in Actuarial Sciences, Finance, Medicine, Welfare analysis, etc. are garthered in classes of Weighted Mean Loss or Gain (WMLG) statistics. Some of them are Upper Threshold Based (UTH) or…
Let $\left\{ S_{n},n\geq 0\right\} $ be a random walk whose increment distribution belongs without centering to the domain of attraction of an $% \alpha $-stable law, i.e., there are some scaling constants $a_{n}$ such that the sequence…
We provide a systematic approach for deducing statistical limit laws via martingale-coboundary decomposition, for nonuniformly hyperbolic systems with slowly contracting and expanding directions. In particular, if the associated return time…
We study the extreme value distribution of stochastic processes modeled by superstatistics. Classical extreme value theory asserts that (under mild asymptotic independence assumptions) only three possible limit distributions are possible,…
Statistically self-similar measures on $[0,1]$ are limit of multiplicative cascades of random weights distributed on the $b$-adic subintervals of $[0,1]$. These weights are i.i.d, positive, and of expectation $1/b$. We extend these cascades…
In this short note we study the asymptotic behaviour of the minima over compact intervals of Gaussian processes, whose paths are not necessarily smooth. We show that, beyond the logarithmic large deviation Gaussian estimates, this problem…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…
Classical mathematical statistics deals with models that are parametrized by a Euclidean, i.e. finite dimensional, parameter. Quite often such models have been and still are chosen in practical situations for their mathematical simplicity…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
This article presents various weak laws of large numbers for the so-called realised covariation of a bivariate stationary stochastic process which is not a semimartingale. More precisely, we consider two cases: Bivariate moving average…
In a functional setting, we propose two test statistics to highlight the Poisson nature of a Cox process when n copies of the process are available. Our approach involves a comparison of the empirical mean and the empirical variance of the…
We discuss a complementary asymptotic analysis of the so called minimal random walk. More precisely, we present a version of the almost sure central limit theorem as well as a generalization of the recently proposed quadratic strong laws.…