On the explicit form of the density of Brownian excursion local time
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- by G. Hooghiemstra PDF
- Proc. Amer. Math. Soc. 84 (1982), 127-130 Request permission
Abstract:
Let $\underline W _0^ + (t)$, $0 \leqslant t \leqslant 1$, denote Brownian excursion and let $\underline {l} _0^ + (\upsilon )$, $\upsilon \geqslant 0$, be its local time at level $\upsilon$. Starting from a representation of the density of $\underline {l} _0^ + (\upsilon )$ as a complex integral we derive an explicit form of this density, written as an infinite series involving the $n$-fold convolution of known densities. Finally the result is used as an alternative check of Knight’s result on the same topic.References
- Kai Lai Chung, Excursions in Brownian motion, Ark. Mat. 14 (1976), no. 2, 155–177. MR 467948, DOI 10.1007/BF02385832
- J. W. Cohen and G. Hooghiemstra, Brownian excursion, the $M/M/1$ queue and their occupation times, Math. Oper. Res. 6 (1981), no. 4, 608–629. MR 703101, DOI 10.1287/moor.6.4.608
- R. K. Getoor and M. J. Sharpe, Excursions of Brownian motion and Bessel processes, Z. Wahrsch. Verw. Gebiete 47 (1979), no. 1, 83–106. MR 521534, DOI 10.1007/BF00533253 G. Hooghiemstra, Brownian excursion and limit theorems for the $M/G/1$ queue, Ph.D. thesis, Univ. of Utrecht, 1979.
- Frank B. Knight, On the excursion process of Brownian motion, Trans. Amer. Math. Soc. 258 (1980), no. 1, 77–86. MR 554319, DOI 10.1090/S0002-9947-1980-0554319-6 —, Zbl. Math. 426 (1980), abstract 60073.
Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 127-130
- MSC: Primary 60J65; Secondary 60J55
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633293-5
- MathSciNet review: 633293