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.
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