Persistence of a Two-dimensional Super-brownian Motion in a Catalytic Medium
نویسندگان
چکیده
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 process is nitèuniformly in time'. This is in contrast to thèclassical' super-Brownian motion where this holds only in high dimensions (d 3), whereas in low dimensions the variances grow without bound, and the process clusters leading to local extinction.
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