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2013 The probability law of the Brownian motion normalized by its range
Florin Spinu
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Electron. Commun. Probab. 18: 1-8 (2013). DOI: 10.1214/ECP.v18-2568

Abstract

In the present paper we deduce explicit formulas for the probability laws of the quotients $X_t/R_t$ and $m_t/R_t$, where $X_t$ is the standard Brownian motion and $m_t$, $M_t$, $R_t$ are its running minimum, maximum and range, respectively.The computation makes use of standard techniques from analytic number theory and the theory of the Hurwitz zeta function.

Citation

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Florin Spinu. "The probability law of the Brownian motion normalized by its range." Electron. Commun. Probab. 18 1 - 8, 2013. https://doi.org/10.1214/ECP.v18-2568

Information

Accepted: 13 June 2013; Published: 2013
First available in Project Euclid: 7 June 2016

zbMATH: 1306.60116
MathSciNet: MR3070912
Digital Object Identifier: 10.1214/ECP.v18-2568

Subjects:
Primary: 60J65

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