Related papers: Variable-Length Coding of Two-Sided Asymptotically…
Variable-to-variable length (VV) codes are a class of lossless source coding. As their name implies, VV codes encode a variable-length sequence of source symbols into a variable-length codeword. This paper will give a complete proof of an…
We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also…
The article presents a new interpretation for Zipf-Mandelbrot's law in natural language which rests on two areas of information theory. Firstly, we construct a new class of grammar-based codes and, secondly, we investigate properties of…
We consider a particle system on $Z^d$ with finite state space and interactions of infinite range. Assuming that the rate of change is continuous and decays sufficiently fast, we introduce a perfect simulation algorithm for the stationary…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
This paper studies limit measures of stationary measures of stochastic ordinary differential equations on the Euclidean space and tries to determine which invariant measures of an unperturbed system will survive. Under the assumption for…
We investigate inference of variable-length codes in other domains of computer science, such as noisy information transmission or information retrieval-storage: in such topics, traditionally mostly constant-length codewords act. The study…
The large-deviation method allows to characterize an ergodic counting process in terms of a thermodynamic frame where a free energy function determines the asymptotic non-stationary statistical properties of its fluctuations. Here, we study…
We study the effect of observing a stationary process at irregular time points via a renewal process. We establish a sharp difference in the asymptotic behaviour of the self-normalized sample mean of the observed process depending on the…
Integral expressions are determined for the elastic displacement and stress fields due to stationary or moving dislocation loops in finite samples. These general expressions are valid for anisotropic media as well. Specifically for the…
The recently proposed set-up of source coding with a side information "vending machine" allows the decoder to select actions in order to control the quality of the side information. The actions can depend on the message received from the…
Higher-order spectra (or polyspectra), defined as the Fourier Transform of a stationary process' autocumulants, are useful in the analysis of nonlinear and non Gaussian processes. Polyspectral means are weighted averages over Fourier…
For a non-stationary or non-ergodic marked point process (MPP) on $\R^d$, the definition of averages becomes ambiguous as the process might have a different stochastic behavior in different realizations (non-ergodicity) or in different…
In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to…
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that…
We investigate stationarity and stability of half-spaces as isoperimetric sets for product probability measures, considering the cases of coordinate and non-coordinate half-spaces. Moreover, we present several examples to which our results…
Let $(X_t)_{t \geq 0}$ be a continuous time Markov process on some metric space $M,$ leaving invariant a closed subset $M_0 \subset M,$ called the {\em extinction set}. We give general conditions ensuring either "Stochastic persistence"…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
This paper is the first part of a project devoted to studying the interconnection between controllability properties of a dynamical system and the large-time asymptotics of trajectories for the associated stochastic system. It is proved…
We provide general conditions ensuring that the value functions of some nonlinear stopping problems with finite horizon converge to the value functions of the corresponding problems with infinite horizon. Our result can be formulated as…