Related papers: Maxima of linear processes with heavy-tailed innov…
Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…
In this paper we propose a framework that enables the study of large deviations for point processes based on stationary sequences with regularly varying tails. This framework allows us to keep track not of the magnitude of the extreme…
We consider the limit distribution of maxima of periodograms for stationary processes. Our method is based on $m$-dependent approximation for stationary processes and a moderate deviation result.
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
A maximal inequality is an inequality which involves the (absolute) supremum $\sup_{s\leq t}|X_{s}|$ or the running maximum $\sup_{s\leq t}X_{s}$ of a stochastic process $(X_t)_{t\geq 0}$. We discuss maximal inequalities for several classes…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
We consider the asymptotic behavior of the expectation of the maximum for a special assignment process with constant or i.i.d. coefficients. We show how it depends on the coefficients' distribution.
We extend classical results by A. V. Nagaev [Izv. Akad. Nauk UzSSR Ser. Fiz.--Mat. Nauk 6 (1969) 17--22, Theory Probab. Appl. 14 (1969) 51--64, 193--208] on large deviations for sums of i.i.d. regularly varying random variables to partial…
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…
We derive subexponential tail asymptotics for the distribution of the maximum of a compound renewal process with linear component and of a L\'evy process, both with negative drift, over random time horizon $\tau$ that does not depend on the…
Heavy-tailed distributions are frequently used to enhance the robustness of regression and classification methods to outliers in output space. Often, however, we are confronted with "outliers" in input space, which are isolated observations…
This article investigates the phenomenon of maximal rigidity in spatial processes, where perfect interpolation of the process is possible from partial information, specifically, from its restriction to a strict subdomain, often resulting in…
In the investigation of limits of Markov chains, the presence of states which become instantaneous states in the limit may prevent the convergence of the chain in the Skorohod topology. We present in this article a weaker topology adapted…
This paper deals with the optimal stopping problem under partial observation for piecewise-deterministic Markov processes. We first obtain a recursive formulation of the optimal filter process and derive the dynamic programming equation of…
We propose a stochastic process driven by memory effect with novel distributions including both exponential and leptokurtic heavy-tailed distributions. A class of distribution is analytically derived from the continuum limit of the discrete…
In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…
We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large point heuristic: the limit measure is concentrated on the cone of point measures with one single point. We then…
The paper is dealing with semi-classical asymptotics of a characteristic function for a stochastic process. The main technical tool is provided by the stationary phase method. The extremal range for a stochastic process is defined by limit…
Maxima of moving maxima of continuous functions (CM3) are max-stable processes aimed at modeling extremes of continuous phenomena over time. They are defined as Smith and Weissman's M4 processes with continuous functions rather than…
We study the joint limit distribution of the $k$ largest eigenvalues of a $p\times p$ sample covariance matrix $XX^\T$ based on a large $p\times n$ matrix $X$. The rows of $X$ are given by independent copies of a linear process,…