A time-change approach to Kotani's extension of Yor's formula

• Hariya Yuu

  Research Institute for Mathematical Sciences, Kyoto University

Bibliographic Information

Other Title

• time change approach to Kotani s extension of Yor s formula

Abstract

In [3], Kotani proved analytically that expectations for additive functionals of Brownian motion {B_t, t≥0} of the form <br>E₀ [ f(B_t)g (∫^t₀ φ(B_s)ds) ]<br>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. <br>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.

Journal

• Journal of the Mathematical Society of Japan

  Journal of the Mathematical Society of Japan 58 (1), 129-151, 2006

  The Mathematical Society of Japan

Keywords

• time-changes
• additive functionals of Brownian motion
• 3-dimensional Bessel processes

Details

• CRID: 1390001205116508800
• NII Article ID: 10017178356
• NII Book ID: AA0070177X
• DOI: 10.2969/jmsj/1145287096
• ISSN: 18811167
• ISSN: 18812333
• ISSN: 00255645
• MRID: 2204568
• NDL BIB ID: 7783298
• Web Site: http://id.ndl.go.jp/bib/7783298
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I7783298
• Text Lang: en
• Data Source:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• Abstract License Flag: Disallowed