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- W3100429501 abstract "In [2] foundations for diffusion approximation via Stein’s method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein’s method (see, for example, its use in [1] or [7]). A semigroup argument is used in [2] to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in [2], the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on $D[0,1]$ growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of [2] hold true." @default.
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- W3100429501 date "2017-01-01" @default.
- W3100429501 modified "2023-09-25" @default.
- W3100429501 title "Note on A. Barbour’s paper on Stein’s method for diffusion approximations" @default.
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- W3100429501 doi "https://doi.org/10.1214/17-ecp54" @default.
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