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

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

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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 cartoon martian with big head theory of random processes lets us show that limiting cases read more 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.