Limiting distributions for a class of super-Brownian motions with spatially dependent branching mechanisms
type: Item
instance of: scholarly article
title: Limiting distributions for a class of super-Brownian motions with spatially dependent branching mechanisms
author: Y.-X. Ren
author: Ting Yang
published in: Journal of Theoretical Probability
publication date: 2024-08-24T00:00:00Z
review text: Super-Brownian motion is a particular class of superprocesses that serve as stochastic models for the evolution of a random mass distributed in space. In this paper, the authors establish the almost sure growth rate of the mass located outside a time-dependent interval \((-\delta t,\delta t)\) for \(\delta>0\). This growth rate is characterized in terms of the principal eigenvalue of a Schrödinger-type operator associated with the branching mechanism. The paper also includes additional related results.
Mathematics Subject Classification ID: 60J68
Mathematics Subject Classification ID: 60G57
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 60F05
zbMATH DE Number: 7900855
zbMATH Keywords: super-Brownian motion
zbMATH Keywords: spatially dependent branching mechanism
zbMATH Keywords: growth rate
zbMATH Keywords: convergence in distribution
MaRDI profile type: Publication
cites work: Convergence in law of the minimum of a branching random walk
cites work: Branching Brownian motion seen from its tip
cites work: The extremal process of branching Brownian motion
cites work: Anomalous spreading in reducible multitype branching Brownian motion
cites work: Limiting distribution of particles near the frontier in the catalytic branching Brownian motion
cites work: Branching Brownian motion with catalytic branching at the origin
cites work: Limiting distribution of the rightmost particle in catalytic branching Brownian motion
cites work: Law of large numbers for branching symmetric hunt processes with measure-valued branching rates
cites work: Skeleton decomposition and law of large numbers for supercritical superprocesses
cites work: From Brownian Motion to Schrödinger’s Equation
cites work: Superprocesses and partial differential equations
cites work: Branching exit Markov systems and superprocesses
cites work: \(\mathbb{N}\)-measures for branching exit Markov systems and their applications to differential equations
cites work: Spines, skeletons and the strong law of large numbers for superdiffusions
cites work: On the construction and support properties of measure-valued diffusions on \(D\subseteq \mathbb{R}^d\) with spatially dependent branching
cites work: Q4027479
cites work: Minimal position and critical martingale convergence in branching random walks, and directed polymers on disordered trees
cites work: Q2774021
cites work: Random Measures, Theory and Applications
cites work: The Backbone Decomposition for Spatially Dependent Supercritical Superprocesses
cites work: Traveling waves in inhomogeneous branching Brownian motions. I
cites work: Measure-Valued Branching Markov Processes
cites work: Convergence in law for the branching random walk seen from its tip
cites work: Limiting distributions for particles near the frontier of spatially inhomogeneous branching Brownian motions
cites work: Limiting distributions for the maximal displacement of branching Brownian motions
cites work: Law of large numbers for supercritical superprocesses with non-local branching
cites work: The extremal process of super-Brownian motion
cites work: Exponential growth of the numbers of particles for branching symmetric \(\alpha\)-stable processes
cites work: Spread rate of branching Brownian motions
cites work: Maximal displacement and population growth for branching Brownian motions
DOI: 10.1007/S10959-023-01304-2
description: scientific article; zbMATH DE number 7900855