Some large-deviation theorems for branching diffusions
type: Item
instance of: scholarly article
title: Some large-deviation theorems for branching diffusions
zbMATH Open document ID: 0759.60024
author: Tzong-Yow Lee
published in: The Annals of Probability
publication date: 1993-01-17T00:00:00Z
review text: A branching diffusion process is studied when its diffusivity decreases to 0 at the rate of \(\varepsilon<<1\) and its branching-transmutation intensity increases at the rate of \(\varepsilon^{-1}\). The author derives the action functionals which describe some large deviations of the processes as \(\varepsilon\to 0\). In particular, the asymptotic probability as \(\varepsilon\to 0\) that the sample tree contains a branch close to a given function \(\varphi(t)\), and the asymptotic probability that the sample tree contains a 2-branch close to given functions \((\varphi_ 1(t),\varphi_ 2(t))\) are obtained.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J80
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 35B25
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 97396
zbMATH Keywords: large-deviation theorems
zbMATH Keywords: branching diffusion process
zbMATH Keywords: action functionals
reviewed by: Aleksandr D. Borisenko
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176989692
OpenAlex ID: W2052083791
DOI: 10.1214/AOP/1176989692
description: scientific article; zbMATH DE number 97396