Asymptotic Results for Rough Continuous-state Branching Processes

TL;DR

This paper derives explicit Laplace transform representations for extinction times and total progeny in rough continuous-state branching processes, revealing their tail distributions are significantly heavier than those of classical Feller diffusions.

Contribution

It provides explicit formulas for key probabilistic quantities of rough continuous-state branching processes and compares their tail behaviors to classical models.

Findings

Laplace transforms of extinction time and total progeny are explicitly characterized.

Tail distributions of rough processes are much heavier than Feller diffusions.

The results enhance understanding of the probabilistic structure of rough branching processes.

Abstract

In this paper we provide explicit representations of Laplace transforms of extinction time and total progeny of rough continuous-state branching processes introduced in [7]. Also, we show that their tail distributions are much fatter than those of Feller branching diffusions.