On Random Population Growth Punctuated by Geometric Catastrophic Events

Catastrophe Markov chain population models have received a lot of attention in the recent past. Besides systematic random immigration events promoting growth, we study a particular case of populations simultaneously subject to the effect of geometric catastrophes that cause recurrent mass removal. We describe the subtle balance between the two such contradictory effects.

QUENCHED LARGE DEVIATION FOR SUPER-BROWNIAN MOTION WITH RANDOM IMMIGRATION

Quenched local large deviation is derived for the super-Brownian motion with super-Brownian immigration, in dimension d ≥ 4. At the critical dimension d = 4, the quenched and annealed LDP are of the same speed but are different rate.

A note on two-level superprocesses

We prove some central limit theorems for a two-level super-Brownian motion with random immigration, which lead to limiting Gaussian random fields. The covariances of those Gaussian fields are explicitly characterized.

Large deviations for super-Brownian motion with immigration

We derive a large-deviation principle for super-Brownian motion with immigration, where the immigration is governed by the Lebesgue measure. We show that the speed function ist1/2ford= 1,t/logtford= 2 andtford≥ 3, which is different from that of the occupation-time process counterpart (without immigration) and the model of random immigration.

Large deviations for super-Brownian motion with immigration

We derive a large-deviation principle for super-Brownian motion with immigration, where the immigration is governed by the Lebesgue measure. We show that the speed function is t1/2 for d = 1, t/logt for d = 2 and t for d ≥ 3, which is different from that of the occupation-time process counterpart (without immigration) and the model of random immigration.