Work

Convergence of Limiting Cases of Continuous-Time, Discrete-Space Jump Processes to Diffusion Processes for Bayesian Inference

Year: 2025

Type: article

Abstract: Jump-diffusion algorithms are applied to sampling from Bayesian posterior distributions. We consider a class of random sampling algorithms based on continuous-time jump processes. The semigroup theory of random processes lets us show that limiting cases of certain jump processes acting on discretized spaces converge to diffusion processes as the discretization is refined. One of these processes leads to the familiar Langevin diffusion equation; another leads to an entirely new diffusion equation.

Source: Mathematics

DOI: 10.3390/math13071084

Author: Aaron Lanterman

Institution: Georgia Institute of Technology

Language: English

Topic: Markov Chains and Monte Carlo Methods

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: Air Force Office of Scientific Research, Army Research Office