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JANUARY, 2006 A time-change approach to Kotani's extension of Yor's formula
Yuu HARIYA
J. Math. Soc. Japan 58(1): 129-151 (JANUARY, 2006). DOI: 10.2969/jmsj/1145287096

Abstract

In [3], Kotani proved analytically that expectations for additive functionals of Brownian motion {Bt,t0} of the form E 0 f ( B t ) g 0 t φ ( B s ) d s have the asymptotics t-3/2 as t for some suitable non-negative functions φ, f and g. This generalizes, in the asymptotic form, Yor's explicit formula [10] for exponential Brownian functionals.

In the present paper, we discuss this generalization probabilistically, by using a time-change argument. We may easily see from our argument that this asymptotics t-3/2 comes from the transition probability of 3-dimensional Bessel process.

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Yuu HARIYA. "A time-change approach to Kotani's extension of Yor's formula." J. Math. Soc. Japan 58 (1) 129 - 151, JANUARY, 2006. https://doi.org/10.2969/jmsj/1145287096

Information

Published: JANUARY, 2006
First available in Project Euclid: 17 April 2006

zbMATH: 1093.60052
MathSciNet: MR2204568
Digital Object Identifier: 10.2969/jmsj/1145287096

Subjects:
Primary: 60J65
Secondary: 60F99 , 60J55

Keywords: 3-dimensional Bessel processes , additive functionals of Brownian motion , time-changes

Rights: Copyright © 2006 Mathematical Society of Japan

Vol.58 • No. 1 • JANUARY, 2006
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