Conditioned super-Brownian motion
type: Item
instance of: scholarly article
title: Conditioned super-Brownian motion
zbMATH Open document ID: 0792.60037
DOI: 10.1007/BF01200209
author: L. Overbeck
publication date: 1994-07-14T00:00:00Z
review text: We investigate classes of conditioned super-Brownian motions, namely \(H\)- transforms \(P^ H\) with nonnegative finitely-based space-time harmonic functions \(H(t,\mu)\). We prove that \(P^ H\) is the unique solution of a martingale problem with interaction and is a weak limit of a sequence of rescaled interacting branching Brownian motions. We identify the limit behaviour of \(H\)-transforms with functions \(H(t,\mu) = h(t,\mu(1))\) depending only on the total mass \(\mu(1)\). Using the Palm measures of the super-Brownian motion we describe for an additive space-time harmonic function \(H(t,\mu) = \int h(t,x)\) \(\mu(dx)\) the \(H\)-transform \(P^ H\) as a conditioned super-Brownian motion in which an immortal particle moves like an \(h\)-transform of Brownian motion.
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60J50
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60J80
zbMATH DE Number: 568996
zbMATH Keywords: \(h\)-transform of Brownian motion
zbMATH Keywords: super-Brownian motions
zbMATH Keywords: martingale problem
zbMATH Keywords: limit behaviour
zbMATH Keywords: Palm measures
MaRDI profile type: Publication
cites work: Growing conditioned trees
cites work: Super-Brownian motion: Path properties and hitting probabilities
cites work: Q5658888
cites work: Sufficient statistics and extreme points
cites work: Regular Transition Functions and Regular Superprocesses
cites work: Q1177210
cites work: Hedging and Maxmin
cites work: Q3721531
cites work: Measure-valued Markov branching processes conditioned on non-extinction
cites work: Absolute Continuity Results for Superprocesses with Some Applications
cites work: Persistence of critical multitype particle and measure branching processes
cites work: A weighted occupation time for a class of measure-valued branching processes
cites work: Multivariate point processes: predictable projection, Radon-Nikodym derivatives, representation of martingales
cites work: Q4114580
cites work: Q5653423
cites work: Q4279420
cites work: A criterion of convergence of measure‐valued processes: application to measure branching processes
cites work: Q4734585
cites work: Construction et Propriétés de Martingales des Branchements Spatiaux Interactifs
cites work: A limit theorem of branching processes and continuous state branching processes
published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 568996