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@article{Kasprzak:2017:10.1214/17-ecp54,
author = {Kasprzak, MJ and Duncan, AB and Vollmer, SJ},
doi = {10.1214/17-ecp54},
journal = {Electronic Communications in Probability},
title = {Note on A. Barbour’s paper on Stein’s method for diffusion approximations},
url = {http://dx.doi.org/10.1214/17-ecp54},
volume = {22},
year = {2017}
}

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TY  - JOUR
AB  - 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.
AU  - Kasprzak,MJ
AU  - Duncan,AB
AU  - Vollmer,SJ
DO  - 10.1214/17-ecp54
PY  - 2017///
SN  - 1083-589X
TI  - Note on A. Barbour’s paper on Stein’s method for diffusion approximations
T2  - Electronic Communications in Probability
UR  - http://dx.doi.org/10.1214/17-ecp54
UR  - http://hdl.handle.net/10044/1/64427
VL  - 22
ER  -

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