Journal•ISSN: 1980-0436

# ALEA-Latin American Journal of Probability and Mathematical Statistics

About: ALEA-Latin American Journal of Probability and Mathematical Statistics is an academic journal. The journal publishes majorly in the area(s): Random walk & Central limit theorem. It has an ISSN identifier of 1980-0436. Over the lifetime, 400 publication(s) have been published receiving 2954 citation(s).

Topics: Random walk, Central limit theorem, Poisson distribution, Limit (mathematics), Random variable

##### Papers published on a yearly basis

##### Papers

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TL;DR: In this paper, a system of d coupled nonlinear stochastic heat equations in spatial dimension 1 driven by d-dimensional additive space-time white noise is considered, and upper and lower bounds on hitting probabilities of the solution are established in terms of respectively Hausdorff measure and Newtonian capacity.

Abstract: We consider a system of d coupled non-linear stochastic heat equations in spatial dimension 1 driven by d-dimensional additive space-time white noise. We establish upper and lower bounds on hitting probabilities of the solution {u(t , x)}t∈R+,x∈[0 ,1], in terms of respectively Hausdorff measure and Newtonian capacity. We also obtain the Hausdorff dimensions of level sets and their projections. A result of independent interest is an anisotropic form of the Kolmogorov continuity theorem. AMS 2000 subject classifications: Primary: 60H15, 60J45; Secondary: 60G60.

89 citations

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TL;DR: In this article, a genetic type interacting particle system algorithm and a genealogical model for estimating a class of rare events arising in physics and network analysis is presented. But the authors do not consider how to estimate the probability of the corresponding rare events as well as the distribution of the process.

Abstract: We present in this article a genetic type interacting particle systems algorithm and a genealogical model for estimating a class of rare events arising in physics and network analysis. We represent the distribution of a Markov process hitting a rare target in terms of a Feynman-Kac model in path space. We show how these branching particle models described in previous works can be used to estimate the probability of the corresponding rare events as well as the distribution of the process in this regime.

88 citations

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TL;DR: In this article, a new construction of the Uniform Infinite Planar Quadrangulation (UIPQ) is introduced, based on an extension of the Cori-Vauquelin-Schaeffer mapping in the context of infinite trees.

Abstract: We introduce a new construction of the Uniform Infinite Planar Quadrangulation (UIPQ). Our approach is based on an extension of the Cori-Vauquelin-Schaeffer mapping in the context of infinite trees, in the spirit of previous work on this topic. However, we release the positivity constraint on the labels of trees which was imposed so far, so that our construction is technically much simpler. This approach allows us to prove the conjectures of Krikun pertaining to the "geometry at infinity" of the UIPQ, and to derive new results about the UIPQ, among which a fine study of infinite geodesics.

58 citations

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TL;DR: In this paper, a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field is considered, and it is assumed that E(F 4 4 ) is a Gaussian distribution.

Abstract: Let fFn : n > 1g be a normalized sequence of random variables in some fixed Wiener chaos associated with a general Gaussian field, and assume that E(F 4

58 citations

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TL;DR: In this article, the authors revisited functional central limit theorems for additive functionals of ergodic Markov diffusion processes, translating them as diffusion limits in the asymptotic analysis of Fokker-Planck type equations.

Abstract: We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as diffusion limits in the asymptotic analysis of Fokker-Planck type equations. We focus on the square integrable framework, and we provide tractable conditions on the infinitesimal generator, including degenerate or anomalously slow diffusions. We take advantage on recent developments in the study of the trend to the equilibrium of ergodic diffusions. We discuss examples and formulate open problems.

57 citations