论文标题
关于布格罗尔法律身份的二维扩展
On two-dimensional extensions of Bougerol's identity in law
论文作者
论文摘要
令$ b = \ {b_ {t} \} _ {t \ ge 0} $为一维标准的布朗尼运动，并用$ a_ {t}，\，t \ ge 0 $表示，$ e^{b_ {t}}，t \ ge 0 $，t \ ge 0 $。著名的布格果法律的身份（1983）断言，如果$β= \ {β_{t} \} _ {t \ ge 0} $是独立于$ b $的另一种布朗运动，则$β_{a_ {t}} $与$ \ sinh b_ { Bertoin，Dufresne和Yor（2013）获得了涉及的身份的二维扩展，因为第二次在当地时代$ b $和$β$的当地时间和$β$在level nevel nevel so中。在本文中，我们在当地时代的水平不限于零的情况下提出了它们扩展的概括。我们的论点为原始扩展提供了简短的基本证明，并为这种微妙的身份提供了新的启示。
Let $B=\{ B_{t}\} _{t\ge 0}$ be a one-dimensional standard Brownian motion and denote by $A_{t},\,t\ge 0$, the quadratic variation of $e^{B_{t}},\,t\ge 0$. The celebrated Bougerol's identity in law (1983) asserts that, if $β=\{ β_{t}\} _{t\ge 0}$ is another Brownian motion independent of $B$, then $β_{A_{t}}$ has the same law as $\sinh B_{t}$ for every fixed $t>0$. Bertoin, Dufresne and Yor (2013) obtained a two-dimensional extension of the identity involving as the second coordinates the local times of $B$ and $β$ at level zero. In this paper, we present a generalization of their extension in a situation that the levels of those local times are not restricted to zero. Our argument provides a short elementary proof of the original extension and sheds new light on that subtle identity.
