Limit theorems for conditioned multitype Dawson-Watanabe processes and Feller diffusions

Class of Limit Theorems for Singular Diffusions

Functional Limit Theorems for Multitype Branching Processes and Generalized Pólya Urns

A functional limit theorem is proved for multitype continuous time Markov branching processes. As consequences, we obtain limit theorems for the branching process stopped by some stopping rule, for example when the total number of particles reaches a given level. Using the Athreya–Karlin embedding, these results yield asymptotic results for generalized Pólya urns. We investigate such results in...

Some Local Approximations of Dawson – Watanabe

Let ξ be a Dawson–Watanabe superprocess in R such that ξt is a.s. locally finite for every t ≥ 0. Then for d ≥ 2 and fixed t > 0, the singular random measure ξt can be a.s. approximated by suitably normalized restrictions of Lebesgue measure to the ε-neighborhoods of supp ξt. When d ≥ 3, the local distributions of ξt near a hitting point can be approximated in total variation by those of a stat...

Limit Theorems for Renewal Processes

This article describes the Key renewal theorem and the Blackwell’s renewaltheorem. These two limit theorems for renewal processes are equivalent but of different forms.They are particularly useful for characterizing the asymptotic behavior of a probabilisticquantity of interest in a renewal process. We present two applications of these limit theorems:the limiting distributions o...

Central limit theorems for additive functionals of ergodic Markov diffusions processes

We revisit functional central limit theorems for additive functionals of ergodic Markov diffusion processes. Translated in the language of partial differential equations of evolution, they appear as diffusion limits in the asymptotic analysis of FokkerPlanck type equations. We focus on the square integrable framework, and we provide tractable conditions on the infinitesimal generator, including...