Limit Theorems for Some Critical Superprocesses

Abstract

In this paper we establish some conditional limit theorems for some critical superprocesses $X=\{X_t,t\ge 0\}$. First we identify the rate of non-extinction. Then we show that, for a large class of functions $f$, conditioned on non-extinction at time $t$, the limit, as $t\to \infty$, of $t^{-1}⟨f,X_t⟩$ exists in distribution and we identify this limit. Finally, we also establish, under some conditions, a central limit theorem for $⟨f,X_t⟩$ conditioned on non-extinction at time $t$.

References in corpus (1)

• Dirichlet Heat Kernel Estimates for Rotationally Symmetric Lévy processes

Cited by in corpus (2)

• Central Limit Theorems for Supercritical Branching Nonsymmetric Markov Processes
• Strong law of large numbers for supercritical superprocesses under second moment condition