Note on A. Barbour’s paper on Stein’s method for diffusion approximations

Kasprzak, Mikołaj J, Duncan, Andrew B and Vollmer, Sebastian J (2017) Note on A. Barbour’s paper on Stein’s method for diffusion approximations. Electronic Communications in Probability, 22 (3). pp. 1-8. ISSN 1083-589X

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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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Research Centres and Groups: Probability and Statistics Research Group
Subjects: Q Science > QA Mathematics
Depositing User: Billy Wichaidit
Date Deposited: 15 Jun 2017 09:58
Last Modified: 01 Jul 2017 21:16
URI: http://sro.sussex.ac.uk/id/eprint/68619

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