## ＜プレプリント＞A time-change approach to Kotani’s extension of Yor’s formula

作成者 作成者名 所属機関 所属機関名 Research Institute for Mathematical Sciences, Kyoto University 京都大学数理解析研究所 英語 Faculty of Mathematics, Kyushu University 九州大学大学院数理学研究院 2005-05-17 MHF2005-21 Author's Original open access In [3], Kotani proved analytically that expectations for additive functionals of Brownian motion ${B_t, t geq 0}$ of the form $E_0[f(B_t)g( int_0^t \varphi(B_s)ds)]$ have the asymptotics $t^{-3}/...2$ as $t \rigtarrow infty$ for some suitable non-negative functions $\varphi$, $f$ and $g$. This generalizes, in the asymptotic form, Yor’s explicit formula [9] 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.続きを見る

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レコードID 3367 査読無 MHF Preprint Series || MHF2005-21 || p1-22 http://www.math.kyushu-u.ac.jp/gakufu/ Time-changes Additive functionals of Brownian motion 3-dimensional Bessel processes 60J65 60J55 60F99 Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality 九州大学21世紀COEプログラム「機能数理学の構築と展開」 プレプリント 2009.04.22 2018.02.23