Limit Theorems for Some Critical Superprocesses

2014/03/06 by Ren, Yan-Xia, Song, Renming, Zhang, Rui
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1403.1342

Abstract

In this paper we establish some conditional limit theorems for some critical superprocesses X=\X_t, t≥ 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→∞, 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.

Related

• Limit theorems for a class of critical superprocesses with stable branching
• Subcritical superprocesses conditioned on non-extinction
• Spine decompositions and limit theorems for a class of critical superprocesses
• On properties of a class of strong limits for supercritical superprocesses
• Central Limit Theorems for Super-OU Processes