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Intelligent Robots: State EstimationReasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Mixed Discrete/Continuous Search
Parameter Estimation for Partially Observed Stable Continuous-State Branching Processes
🤖 AI Summary
This paper addresses the challenge of parameter estimation for stable continuous-state branching processes (CSBPs) under partial observation. We propose a novel inference framework grounded in the subordinator representation of CSBPs. Our core innovation lies in fully mapping the stochastic dynamics of CSBPs into the subordinator domain, thereby circumventing reliance on closed-form transition densities. Specifically, we reconstruct the likelihood function assumption-free via Laplace transforms and their numerical inversion, while simultaneously developing a differentiable discrete-time trajectory simulator. The method achieves statistical consistency and computational feasibility for stable CSBPs, markedly improving both estimation accuracy and efficiency. To our knowledge, this is the first approach enabling end-to-end parameter inference and simulation within the subordinator domain.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Estimating parameters of Continuous-State Branching Processes using subordinator representation
Enabling likelihood recovery via Laplace transform inversion without closed-form densities
Proposing a dynamic simulation framework for generating discrete-time CSBP trajectories
Innovation
Methods, ideas, or system contributions that make the work stand out.
Leveraging subordinator representation for parameter estimation
Reformulating dynamics to enable parametric estimation without assumptions
Using Laplace transform inversion for efficient likelihood recovery
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