Parameter Estimation for Partially Observed Stable Continuous-State Branching Processes
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.
Cite
@article{arxiv.2512.13841,
title = {Parameter Estimation for Partially Observed Stable Continuous-State Branching Processes},
author = {Eduardo Gutiérrez-Peña and Carlos Octavio Pérez-Mendoza and Alan Riva Palacio and Arno Siri-Jégousse},
journal= {arXiv preprint arXiv:2512.13841},
year = {2025}
}