Rescaled interacting diffusions converge to super Brownian motion

DOI10.1214/aoap/1050689591zbMath1030.60090OpenAlexW2152614292MaRDI QIDQ1413677

Achim Klenke, J. Theodore Cox

Publication date: 17 November 2003

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aoap/1050689591

zbMATH Keywords

martingale problemdiffusion limitlong range limitspatially rescaled particle systems

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Random measures (60G57) Branching processes (Galton-Watson, birth-and-death, etc.) (60J80)

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Cites Work

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• Infinite dimensional stochastic differential equations and their applications
• An interacting system in population genetics. I
• Rescaled contact processes converge to super-Brownian motion in two or more dimensions
• Ergodic theorems for infinite systems of locally interacting diffusions
• Rescaled voter models converge to super-Brownian motion.
• Stochastic p.d.e.'s arising from the long range contact and long range voter processes
• Comparison of interacting diffusions and an application to their ergodic theory
• Ergodic theorems for coupled random walks and other systems with locally interacting components
• On the Attracting Orbit of a Non-Linear Transformation Arising From Renormalization Of Hierarchically Interacting Diffusions Part I: The Compact Case

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