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Note on A. Barbour’s paper on Stein’s method for diffusion approximations
journal contribution
posted on 2023-06-09, 06:43 authored by Mikolaj J Kasprzak, Andrew B Duncan, Sebastian J VollmerIn [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.
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- Published
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- Published version
Journal
Electronic Communications in ProbabilityISSN
1083-589XPublisher
Institute of Mathematical StatisticsExternal DOI
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3Volume
22Page range
1-8Department affiliated with
- Mathematics Publications
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- Probability and Statistics Research Group Publications
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- Yes
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2017-06-15First Open Access (FOA) Date
2017-06-15First Compliant Deposit (FCD) Date
2017-06-15Usage metrics
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