On the Occupation Time of Brownian Excursion

Gerard Hooghiemstra (Technical University Delft)

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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Pages: 61-64

Publication Date: August 4, 1999

DOI: 10.1214/ECP.v4-1006

References

  1. K.L. Chung, Excursions in Brownian motion, Ark. Math. 14, (1976), 155--177. Math Review link
  2. 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
  3. R.K. Getoor and M.J. Sharpe, Excursions of Brownian motion and Bessel processes, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 47, (1979), 83--106. Math Review link
  4. G. Hooghiemstra, Brownian Excursion and Limit Theorems for the M/G/1 queue, Ph.D. thesis University Utrecht, (1979). Math. Review number not available.
  5. 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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