关于BM（$μ$）和BES的指数积分泛函（3）
On some exponential integral functionals of BM($μ$) and BES(3)
摘要：
本文导出了积分泛函$$ \int_0^\infty (p(\exp(B^{(μ)}_t)+1)^{-1}+ q(\exp(B^{(μ)}_t)+1)^{-2}) dt, $$ $$ \int_0^\infty (p(\exp(R^{(3)}_t)-1)^{-1}+ q(\exp(R^{(3)}_t)-1)^{-2}) dt, $$的Laplace变换，其中$p$和$q$均为实数，$\{B^{(μ)}_t: t\geq 0\}$为漂移布朗运动，$μ>0,$ BM（$μ$），$\{R^{(3)}_t: t\geq 0\}$为三维贝塞尔过程BES（3）.这些变换是用高斯超几何函数给出的，并且这些结果与Jacobi扩散的某些泛函密切相关。这一工作推广和完善了Donati-Martin和Yor以及Salminen和Yor的一些结果。
英文摘要：
In this paper we derive the Laplace transforms of the integral functionals $$ \int_0^\infty (p(\exp(B^{(μ)}_t)+1)^{-1}+ q(\exp(B^{(μ)}_t)+1)^{-2}) dt, $$ $$ \int_0^\infty (p(\exp(R^{(3)}_t)-1)^{-1}+ q(\exp(R^{(3)}_t)-1)^{-2}) dt, $$ where $p$ and $q$ are real numbers, $\{B^{(μ)}_t: t\geq 0\}$ is a Brownian motion with drift $μ>0,$ BM($μ$), and $\{R^{(3)}_t: t\geq 0\}$ is a 3-dimensional Bessel process, BES(3). The transforms are given in terms of Gauss' hypergeometric functions and it is seen that the results are closely related to some functionals of Jacobi diffusions. This work generalizes and completes some results of Donati--Martin and Yor and Salminen and Yor.
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