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

Aaron Lanterman ()
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Aaron Lanterman: School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

Mathematics, 2025, vol. 13, issue 7, 1-10

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.

Keywords: Markov chain Monte Carlo; Metropolis–Hastings; Gibbs sampling; pattern theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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