Parameter Estimation for Partially Observed Stable Continuous-State Branching Processes

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.

💡 Research Summary

This paper introduces a novel inference framework for estimating the parameters of continuous‑state branching processes (CSBPs) by exploiting their representation as subordinators. The authors observe that the Laplace transform of a CSBP satisfies
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