Rescaled Lotka–Volterra models converge to super-Brownian motion

Rescaled Lotka-Volterra Models Converge to Super Stable Processes

Recently, it has been shown that stochastic spatial Lotka-Volterra models when suitably rescaled can converge to a super Brownian motion. We show that the limit process could be a super stable process if the kernel of the underlying motion is in the domain of attraction of a stable law. The corresponding results in Brownian setting were proved by Cox and Perkins (2005, 2008). As applications of...

Avoiding-probabilities for Brownian Snakes and Super-brownian Motion Avoiding-probabilities for Brownian Snakes and Super-brownian Motion

We investigate the asymptotic behaviour of the probability that a normalized d-dimensional Brownian snake (for instance when the lifetime process is an excursion of height 1) avoids 0 when starting at distance " from the origin. In particular we show that when " tends to 0, this probability respectively behaves (up to multiplicative constants) like " 4 , " 2 p 2 and " (p 17?1)=2 , when d = 1, d...

Avoiding-probabilities for Brownian snakes and super-Brownian motion

We investigate the asymptotic behaviour of the probability that a normalized d-dimensional Brownian snake (for instance when the life-time process is an excursion of height 1) avoids 0 when starting at distance ε from the origin. In particular we show that when ε tends to 0, this probability respectively behaves (up to multiplicative constants) like ε, ε √ 2 and ε √ 17−1)/2, when d = 1, d = 2 a...

Biodiversity of Catalytic Super-Brownian Motion

In this paper we investigate the structure of the equilibrium state of three{dimensional catalytic super-Brownian motion where the catalyst is itself a classical super-Brownian motion. We show that the reactant has an in nite local biodiversity or genetic abundance. This contrasts the nite local biodiversity of the equilibrium of classical super-Brownian motion. Another question we address is t...

The average density of super-Brownian motion