Electronic Communications in Probability

On the one-sided exit problem for fractional Brownian motion

Frank Aurzada

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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

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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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