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The occupation time of Brownian motion in a ball |
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| Authors: | J. -C. Gruet Z. Shi |
| Affiliation: | (1) Laboratoire de Probabilités, CNRS URA 224, Université Paris VI, Tour 56, 4 Place Jussieu, 75252, Paris Cedex 05, France;(2) UFR Sciences, Université de Reims Champagne Ardenne, B. P. 347, 51062 Reims Cedex, France;(3) L.S.T.A.-CNRS URA 1321, Université Paris VI, Tour 45-55, 3e étage, 4 Place Jussieu, 75252 Paris Cedex 05, France |
| 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. |
| Keywords: | Occupation time Lé vy's lower class Wiener process |
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