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On the Occupation Time of Brownian Excursion
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Gerard Hooghiemstra, Technical University Delft
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Abstract
Recently, Kalvin M. Jansons derived
in an elegant way the Laplace transform of the time spent by an
excursion above a given level $a>0$. This result can also be
derived from previous work of the author on the occupation time
of the excursion in the interval $(a,a+b]$, by sending $b to
infty$. Several alternative derivations areincluded.
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Full text: PDF
Pages: 61-64
Published on: August 4, 1999
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Bibliography
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K.L. Chung,
Excursions in Brownian motion,
Ark. Math. 14, (1976), 155--177.
Math Review link
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J.W. Cohen and G. Hooghiemstra,
Brownian excursion, the M/M/1 queue and their occupation times,
Math. Oper. Res. 6, (1981), 608--629.
Math Review link
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R.K. Getoor and M.J. Sharpe,
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Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 47, (1979), 83--106.
Math Review link
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G. Hooghiemstra,
Brownian Excursion and Limit Theorems for the M/G/1 queue,
Ph.D. thesis University Utrecht, (1979).
Math. Review number not available.
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K.M. Jansons,
The distribution of time spent by a standard excursion above
a given level, with applications to ring polymers near a
discontinuity in potential,
Elect. Comm. in Probab. 2, (1997), 53--58.
Math Review link
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Electronic Communications in Probability. ISSN: 1083-589X |
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Context