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pro vyhledávání: '"Durieu, Olivier"'
We investigate first-passage percolation on the lattice $\Z^d$ for dimensions $d \geq 2$. Each edge $e$ of the graph is assigned an independent copy of a non-negative random variable $\tau$. We only assume $\P[\tau=0]0$ is explicit) for the probabili
Externí odkaz:
http://arxiv.org/abs/2407.17855
Autor:
Durieu, Olivier, Wang, Yizao
We consider a stochastic process with long-range dependence perturbed by multiplicative noise. The marginal distributions of both the original process and the noise have regularly-varying tails, with tail indices $\alpha,\alpha'>0$, respectively. The
Externí odkaz:
http://arxiv.org/abs/2005.05001
This article introduces the operator-scaling random ball model, generalizing the isotropic random ball models investigated recently in the literature to anisotropic setup. The model is introduced as a generalized random field and results on weak conv
Externí odkaz:
http://arxiv.org/abs/1807.00214
Autor:
Durieu, Olivier, Wang, Yizao
A family of self-similar and translation-invariant random sup-measures with long-range dependence are investigated. They are shown to arise as the limit of the empirical random sup-measure of a stationary heavy-tailed process, inspired by an infinite
Externí odkaz:
http://arxiv.org/abs/1804.07248
We investigate the randomized Karlin model with parameter $\beta\in(0,1)$, which is based on an infinite urn scheme. It has been shown before that when the randomization is bounded, the so-called odd-occupancy process scales to a fractional Brownian
Externí odkaz:
http://arxiv.org/abs/1710.08058
Autor:
Durieu, Olivier, Wang, Yizao
We propose discrete random-field models that are based on random partitions of $\mathbb{N}^2$. The covariance structure of each random field is determined by the underlying random partition. Functional central limit theorems are established for the p
Externí odkaz:
http://arxiv.org/abs/1709.00934
In this note, we recall main properties of generalized random fields and present a proof of the continuity theorem of Paul L\'evy for generalized random fields in the space of tempered distributions. This theorem was first proved by Fernique (1968) i
Externí odkaz:
http://arxiv.org/abs/1706.09326
Autor:
Durieu, Olivier, Wang, Yizao
Publikováno v:
In Stochastic Processes and their Applications January 2022 143:55-88
Autor:
Durieu, Olivier, Wang, Yizao
We investigate a special case of infinite urn schemes first considered by Karlin (1967), especially its occupancy and odd-occupancy processes. We first propose a natural randomization of these two processes and their decompositions. We then establish
Externí odkaz:
http://arxiv.org/abs/1508.01506
Recently, Hammond and Sheffield introduced a model of correlated random walks that scale to fractional Brownian motions with long-range dependence. In this paper, we consider a natural generalization of this model to dimension $d\geq 2$. We define a
Externí odkaz:
http://arxiv.org/abs/1504.04891