Spatial epidemics and local times for critical branching random walks in dimensions 2 and 3

DOI10.1007/s00440-009-0239-1zbMath1204.92061arXiv0901.0246OpenAlexW2090417942MaRDI QIDQ707605

Steven P. Lalley, Xinghua Zheng

Publication date: 8 October 2010

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.0246

zbMATH Keywords

super-Brownian motionlocal timesbranching random walkDawson-Watanabe processcritical scalingSugitani's theoremWatanabe's theorem

Mathematics Subject Classification ID

Epidemiology (92D30) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Applications of stochastic analysis (to PDEs, etc.) (60H30) Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.) (60J70)

Related Items (10)

Capacity of the range of tree-indexed random walk ⋮ Bootstrap percolation on the product of the two-dimensional lattice with a Hamming square ⋮ The range of tree-indexed random walk in low dimensions ⋮ An upper bound for \(p_c\) in range-\(R\) bond percolation in two and three dimensions ⋮ A phase diagram for a stochastic reaction diffusion system ⋮ A phase transition for measure-valued SIR epidemic processes ⋮ On the maximal displacement of subcritical branching random walks ⋮ On the maximal displacement of near-critical branching random walks ⋮ On the tail of the branching random walk local time ⋮ The dimension of the boundary of super-Brownian motion

Cites Work

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• Occupation statistics of critical branching random walks in two or higher dimensions
• Stochastic partial differential equations for some measure-valued diffusions
• One dimensional stochastic partial differential equations and the branching measure diffusion
• The carrying dimension of a stochastic measure diffusion
• Rescaled contact processes converge to super-Brownian motion in two or more dimensions
• Brownian excursions, critical random graphs and the multiplicative coalescent
• Statistical mechanics of crabgrass
• Some properties for the measure-valued branching diffusion processes
• Explicit stochastic integral representations for historical functionals
• Spatial epidemics: Critical behavior in one dimension
• A limit theorem of branching processes and continuous state branching processes
• Random Walk: A Modern Introduction
• Ergodic theory and a local occupation time for measure-valued critical branching brownian motion
• Critical behavior of some measure-valued processes
• Geostochastic calculus
• The final size of a nearly critical epidemic, and the first passage time of a Wiener process to a parabolic barrier
• Probability Inequalities for Sums of Bounded Random Variables
• Critical scaling for the SIS stochastic epidemic

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