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 Electronic Communications in Probability > Vol. 2 (1997) > Paper 5 open journal systems 


The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential

Kalvis M. Jansons, University College London


Abstract
The law for the time tau_{a} spent by a standard Brownian excursion above a given level a>0 is found using Ito excursion theory. This is achieved by conditioning the excursion to have exactly one mark of an independent Poisson process. Various excursion rates for excursions conditioned to have exactly n marks are also given in terms of generating functions. This work has applications to the theory of ring polymers and end-attached polymers near a discontinuity in potential.


Full text: PDF

Pages: 53-58

Published on: December 5, 1997
Bibliography
  1. Douglas P. Kennedy (1976): The distribution of the maximum Brownian excursion. J. Appl. Probability 13 no. 2, 371--376. Math Review article not available.
  2. Wim Vervaat (1979): A relation between Brownian bridge and Brownian excursion. Ann. Probab. 7, no. 1, 143--149. Math Review link
  3. L.C.G. Rogers and David Williams, Diffusions, Markov Processes and Martingales: Vol. 2, Ito Calculus, John Wiley & Sons, (1987). Math Review link
  4. Kalvis M. Jansons and L.C.G. Rogers (1991): Probability theory and polymer physics, J. Stat. Phys. 65, 139--165. Math Review link
















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Electronic Communications in Probability. ISSN: 1083-589X