Journal of the Mathematical Society of Japan
Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645
A time-change approach to Kotani's extension of Yor's formula
Yuu Hariya
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2006 年 58 巻 1 号 p. 129-151

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In [3], Kotani proved analytically that expectations for additive functionals of Brownian motion {Bt, t≥0} of the form
E0 [ f(Bt)g (∫t0 φ(Bs)ds) ]
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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© 2006 The Mathematical Society of Japan
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