Abstract
We reconfirm some classical results that the local time process is a proper scale to find limits of additive functionals of Brownian motion [7] (Chapter 6.8, (10)), and we use the excursion theory to prove the corresponding central limit theorem.
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Notes
We use BES\((\delta )\) to denote the Bessel process of dimension \(\delta \).
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The author is grateful to the Mathematics Division of the National Center for Theoretical Sciences (Taiwan) and the Institute of Mathematics of Academia Sinica (Taiwan) for their hospitality and support during her visits.
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Yen, JY. Limit theorems of Brownian additive functionals. Japan J. Indust. Appl. Math. 40, 809–822 (2023). https://doi.org/10.1007/s13160-022-00559-2
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DOI: https://doi.org/10.1007/s13160-022-00559-2