A rough super-Brownian motion

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

Super-brownian Motion with Reflecting Historical Paths

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In p...