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CONSISTENT INFERENCE FOR DIFFUSIONS FROM LOW FREQUENCY MEASUREMENTS
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DOI：10.1214/24-AOS2357.png)
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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
Keyword:
Bayesian inverse problems
reflected diffusion process
spectral PCA
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3.7
论文数:
2.8K
被引数:
2.9W
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