Electronic Communications in Probability

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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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.

Article information

Source
Electron. Commun. Probab., Volume 2 (1997), paper no. 5, 53-58.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1453832500

Digital Object Identifier
doi:10.1214/ECP.v2-984

Mathematical Reviews number (MathSciNet)
MR1484555

Zentralblatt MATH identifier
0890.60074

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Standard Brownian Excursions Brownian Bridges Ring Polymers End-Attached Polymers

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Jansons, Kalvis. 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 (1997), paper no. 5, 53--58. doi:10.1214/ECP.v2-984. https://projecteuclid.org/euclid.ecp/1453832500


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References

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