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May 2003 Rescaled interacting diffusions converge to super Brownian motion
J. Theodore Cox, Achim Klenke
Ann. Appl. Probab. 13(2): 501-514 (May 2003). DOI: 10.1214/aoap/1050689591

Abstract

Super Brownian motion is known to occur as the limit of properly rescaled interacting particle systems such as branching random walk, the contact process and the voter model.

In this paper we show that certain linearly interacting diffusions converge to super Brownian motion if suitably rescaled in time and space. The results comprise nearest neighbor interaction as well as long range interaction.

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J. Theodore Cox. Achim Klenke. "Rescaled interacting diffusions converge to super Brownian motion." Ann. Appl. Probab. 13 (2) 501 - 514, May 2003. https://doi.org/10.1214/aoap/1050689591

Information

Published: May 2003
First available in Project Euclid: 18 April 2003

zbMATH: 1030.60090
MathSciNet: MR1970274
Digital Object Identifier: 10.1214/aoap/1050689591

Subjects:
Primary: 60G57 , 60K35
Secondary: 60F05 , 60H10 , 60J80

Keywords: diffusion limit , long range limit , Martingale problem , spatially rescaled particle systems

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 2 • May 2003
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