FD Fengnan Deng

Research Project

Local Limit Theorem and Large Deviations for Branching Process with Immigration

Asymptotic results for branching processes with immigration, including local limits, large deviations, and regime-dependent oscillation behavior.

In Process Large Deviations Branching Processes

Overview

  • Investigates sharp large deviation behavior for branching processes with immigration under different growth rates.
  • Studies probability generating functions as a route to detailed asymptotic structure.
  • Establishes local limit theorems and reveals oscillation behavior in the small-growth regime.

Methods and contribution

This work extends rare-event analysis for branching systems by accounting for immigration, which changes the probabilistic structure and the asymptotic tools needed to study it. Instead of focusing only on exponential-scale decay, the project develops finer local limit behavior as well.

The results are relevant for branching-style applications in population processes and other stochastic systems where immigration or external arrivals play a meaningful role.

Materials

Paper Slides Talk materials not public