Smooth Density Eld of Catalytic Super-brownian Motion

On the Hot Spots of a Catalytic Super-brownian Motion

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...

Persistence of a Two-dimensional Super-brownian Motion in a Catalytic Medium

The super-Brownian motion X % in a super-Brownian medium % constructed in DF96a] is known to be persistent (no loss of expected mass in the longtime behaviour) in dimensions one ((DF96a]) and three ((DF96b]). Here we ll the gap in showing that persistence holds also in the critical dimension two. The key to this result is that in any dimension (d 3); given the catalyst, the variance of the proc...

On the Connected Components of the Support of Super Brownian Motion and of Its Exit Measure

Tribe proved in a previous paper that a typical point of the support of super Brownian motion considered at a xed time is a.s. disconnected from the others when the space dimension is greater than equal to 3. We give here a simpler proof of this result based on Le Gall's Brownian snake. This proof can then be adapted in order to obtain an analogous result for the support of the exit measure of ...

A Super-brownian Motion with a Locally Innnite Catalytic Mass

A super-Brownian motion X in IR with \hyperbolic" branching rate %2(b) = 1=b 2 , b 2 IR; is constructed, which symbolically could be described by the formal stochastic equation dXt = 1 2 Xt dt + p 2%2Xt dWt ; t > 0; (1) (with a space-time white noise dW). Starting at X0 = a ; a 6 = 0; this superprocess X will never hit the catalytic center: There is an increasing sequence of Brownian stopping t...