CONSISTENT INFERENCE FOR DIFFUSIONS FROM LOW FREQUENCY MEASUREMENTS

• 成果类型: Article
• 署名作者: Nickl, Richard
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/24-AOS2357
• 发表日期: 2024
• 页码: 519-549
• 关键词: nonparametric bayesian-inference; hot-spots conjecture; drift estimation; posterior distributions; ergodic diffusions; Inverse problems; rates; contraction; domains; mcmc

摘要

Let (X-t) be a reflected diffusion process in a bounded convex domain in R-d, solving the stochastic differential equation dX(t) = del f(X-t)dt+root 2f(X-t)dW(t), t >= 0, with W-t a d-dimensional Brownian motion. The data X-0, X-D, ..., X-ND consist of discrete measurements and the time interval D between consecutive observations is fixed so that one cannot 'zoom' into the observed path of the process. The goal is to infer the diffusivity f and the associated transition operator P-t,P-f. We prove injectivity theorems and stability inequalities for the maps f bar right arrow P-t, f bar right arrow P-D,P-f, t