Consistent inference for diffusions from low frequency measurements

2022/10/24 by Richard Nickl, Nickl, Richard · 4 citations
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Bayesian Methods and Mixture Models #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Numerical Analysis (math.NA) #Probability (math.PR) #Statistical Methods and Inference #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2210.13008

openalex publication_date 2022/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (X_t) be a reflected diffusion process in a bounded convex domain in \mathbb R^d, solving the stochastic differential equation dX_t = ∇ f(X_t) dt + √(2f (X_t)) dW_t, ~t ≥ 0, with W_t a d-dimensional Brownian motion. The data X₀, 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,f. We prove injectivity theorems and stability inequalities for the maps f ↦ P_t,f ↦ P_D,f, t

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