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1997 The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential
Kalvis Jansons
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Electron. Commun. Probab. 2: 53-58 (1997). DOI: 10.1214/ECP.v2-984

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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Kalvis Jansons. "The Distribution of Time Spent by a Standard Excursion Above a Given Level, with Applications to Ring Polymers near a Discontinuity in Potential." Electron. Commun. Probab. 2 53 - 58, 1997. https://doi.org/10.1214/ECP.v2-984

Information

Accepted: 5 December 1997; Published: 1997
First available in Project Euclid: 26 January 2016

zbMATH: 0890.60074
MathSciNet: MR1484555
Digital Object Identifier: 10.1214/ECP.v2-984

Subjects:
Primary: 60K35

Keywords: Brownian bridges , End-Attached Polymers , Ring Polymers , Standard Brownian Excursions

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