Electronic Communications in Probability

On the one-sided exit problem for fractional Brownian motion

Frank Aurzada

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Abstract

We consider the one-sided exit problem for fractional Brownian motion (FBM), which is equivalent to the question of the distribution of the lower tail of the maximum of FBM on the unit interval. We improve the bounds given by Molchan (1999) and shed some light on the relation to the quantity I studied there.

Article information

Source
Electron. Commun. Probab., Volume 16 (2011), paper no. 36, 392-404.

Dates
Accepted: 9 August 2011
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465261992

Digital Object Identifier
doi:10.1214/ECP.v16-1640

Mathematical Reviews number (MathSciNet)
MR2831079

Zentralblatt MATH identifier
1244.60042

Subjects
Primary: 60G22: Fractional processes, including fractional Brownian motion
Secondary: (60G15 60G18)

Keywords
First passage time fractional Brownian motion lower tail probability one-sided barrier problem one-sided exit problem small value probability survival exponent

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

Citation

Aurzada, Frank. On the one-sided exit problem for fractional Brownian motion. Electron. Commun. Probab. 16 (2011), paper no. 36, 392--404. doi:10.1214/ECP.v16-1640. https://projecteuclid.org/euclid.ecp/1465261992


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References

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