Electronic Communications in Probability

On the dependence of the first exit times on the fluctuations of the domain boundary

Nikolai Dokuchaev

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Abstract

The paper studies first exit times from domains for diffusion processes and their dependence on variations of the boundary. We establish some robustness of the first exit times with respect to the fluctuations of the boundary. More precisely,  we present an estimate of the $L_1$-distance between exit times from two regions via expectations of exit times.

Article information

Source
Electron. Commun. Probab., Volume 20 (2015), paper no. 80, 3 pp.

Dates
Accepted: 2 November 2015
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465321007

Digital Object Identifier
doi:10.1214/ECP.v20-4531

Mathematical Reviews number (MathSciNet)
MR3434197

Zentralblatt MATH identifier
1329.60279

Subjects
Primary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]
Secondary: 60G17: Sample path properties 60J50: Boundary theory 60J60: Diffusion processes [See also 58J65]

Keywords
diffusion processes first exit times variable boundaries

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Dokuchaev, Nikolai. On the dependence of the first exit times on the fluctuations of the domain boundary. Electron. Commun. Probab. 20 (2015), paper no. 80, 3 pp. doi:10.1214/ECP.v20-4531. https://projecteuclid.org/euclid.ecp/1465321007


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References

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  • Krylov, N. V. Controlled diffusion processes. Translated from the Russian by A. B. Aries. Applications of Mathematics, 14. Springer-Verlag, New York-Berlin, 1980. xii+308 pp. ISBN: 0-387-90461-1