Parameter Estimation for Partially Observed Stable Continuous-State Branching Processes

TL;DR

This paper introduces a new inference framework for estimating parameters of Continuous-State Branching Processes by leveraging their subordinator representation, enabling efficient likelihood computation and dynamic simulation without needing closed-form densities.

Contribution

The paper presents a novel subordinator-based estimation method for CSBPs that simplifies likelihood computation and facilitates trajectory simulation.

Findings

Efficient numerical likelihood recovery via Laplace transform inversion.

Flexible parameter estimation without additional assumptions.

Dynamic simulation framework for CSBPs using subordinator structure.

Abstract

In this article, we present a novel inference framework for estimating the parameters of Continuous-State Branching Processes (CSBPs). We do so by leveraging their subordinator representation. Our method reformulates the estimation problem by shifting the stochastic dynamics to the associated subordinator, enabling a parametric estimation procedure without requiring additional assumptions. This reformulation allows for efficient numerical recovery of the likelihood function via Laplace transform inversion, even in models where closed-form transition densities are unavailable. In addition to offering a flexible approach to parameter estimation, we propose a dynamic simulation framework that generates discrete-time trajectories of CSBPs using the same subordinator-based structure.