Abstract
We show that a sequence of stochastic spatial Lotka-Volterra models, suitably rescaled in space and time, converges weakly to super-Brownian motion with drift. The result includes both long range and nearest neighbor models, the latter for dimensions three and above. These theorems are special cases of a general convergence theorem for perturbations of the voter model.
Original language | English (US) |
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Pages (from-to) | 904-947 |
Number of pages | 44 |
Journal | Annals of Probability |
Volume | 33 |
Issue number | 3 |
DOIs | |
State | Published - May 2005 |
Keywords
- Coalescing random walk
- Lotka-Volterra
- Spatial competition
- Super-Brownian motion
- Voter model
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty