The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 13, Number 2 (2003), 501-514.
Rescaled interacting diffusions converge to super Brownian motion
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.
Ann. Appl. Probab., Volume 13, Number 2 (2003), 501-514.
First available in Project Euclid: 18 April 2003
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G57: Random measures
Secondary: 60F05: Central limit and other weak theorems 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60H10: Stochastic ordinary differential equations [See also 34F05]
Cox, J. Theodore; Klenke, Achim. Rescaled interacting diffusions converge to super Brownian motion. Ann. Appl. Probab. 13 (2003), no. 2, 501--514. doi:10.1214/aoap/1050689591. https://projecteuclid.org/euclid.aoap/1050689591