Abstract
LetW be a Wiener process of dimensiond≥3, starting from 0, and letX(t) be the total time spent byW in the ball centered at 0 with radiust. We give an affirmative answer to a conjecture of Taylor and Tricot(16) on the tail distribution ofX(t). Lévy's lower functions ofX(t) are characterized by an integral test.
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Gruet, J.C., Shi, Z. The occupation time of Brownian motion in a ball. J Theor Probab 9, 429–445 (1996). https://doi.org/10.1007/BF02214658
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DOI: https://doi.org/10.1007/BF02214658