Nonparametric Bayesian inference of discretely observed diffusions

2020/04/09 by Jean-Charles Croix, Croix, Jean-Charles, Masoumeh Dashti +3
Economics, Econometrics and Finance · Mathematics · #35K20 #60J60 #62F15 #62G05 #65N21 #Analysis of PDEs (math.AP) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2004.04636

openalex publication_date 2020/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of the Bayesian inference of drift and diffusion coefficient functions in a stochastic differential equation given discrete observations of a realisation of its solution. We give conditions for the well-posedness and stable approximations of the posterior measure. These conditions in particular allow for priors with unbounded support. Our proof relies on the explicit construction of transition probability densities using the parametrix method for general parabolic equations. We then study an application of these results in inferring the rates of Birth-and-Death processes.

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