Fluctuation limits of multitype branching random fields
type: Item
instance of: scholarly article
title: Fluctuation limits of multitype branching random fields
zbMATH Open document ID: 0749.60079
DOI: 10.1016/0047-259X(92)90090-3
published in: Journal of Multivariate Analysis
publication date: 1992-09-26T00:00:00Z
review text: This paper contains asymptotic results for a system of infinitely many particles of \(k\) different types which immigrate and diffuse in \(R^ d\), and branch according to a multitype law. Three different rescalings are considered: high density, space scaling and space-time scaling. The results are laws of large numbers, functional central limit theorems, and properties of the fluctuation limit processes, which are generalized (i.e., distribution-valued) Ornstein-Uhlenbeck processes (in particular, the generalized Langevin equations they satisfy, regularity of trajectories, large time behaviour and spectral measures). The single type case contains the known results that have been obtained by several authors (including the reviewer).
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 55628
zbMATH Keywords: laws of large numbers
zbMATH Keywords: functional central limit theorems
zbMATH Keywords: fluctuation limit processes
zbMATH Keywords: Ornstein-Uhlenbeck processes
zbMATH Keywords: generalized Langevin equations
zbMATH Keywords: regularity of trajectories
author: José Alfredo López-Mimbela
reviewed by: Luis G. Gorostiza
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 55628