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- W4307316601 abstract "Let $(X_t)$ be a reflected diffusion process in a bounded convex domain in $mathbb R^d$, solving the stochastic differential equation $$dX_t = nabla f(X_t) dt + sqrt{2f (X_t)} dW_t, ~t ge 0,$$ with $W_t$ a $d$-dimensional Brownian motion. The data $X_0, X_D, dots, X_{ND}$ 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 $f mapsto P_{t,f} mapsto P_{D,f}, t<D$. Using these estimates we establish the statistical consistency of a class of Bayesian algorithms based on Gaussian process priors for the infinite-dimensional parameter $f$, and show optimality of some of the convergence rates obtained. We discuss an underlying relationship between the degree of ill-posedness of this inverse problem and the `hot spots' conjecture from spectral geometry." @default.
- W4307316601 created "2022-10-31" @default.
- W4307316601 creator A5091556790 @default.
- W4307316601 date "2022-10-24" @default.
- W4307316601 modified "2023-10-16" @default.
- W4307316601 title "Consistent inference for diffusions from low frequency measurements" @default.
- W4307316601 doi "https://doi.org/10.48550/arxiv.2210.13008" @default.
- W4307316601 hasPublicationYear "2022" @default.
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