论文标题
Girsanov型公式，用于与指数功能相关的布朗运动的一类预期变换
A Girsanov-type formula for a class of anticipative transforms of Brownian motion associated with exponential functionals
论文作者
论文摘要
在本文中，借助Matsumoto-Yor（2000）的结果，我们证明了Girsanov型公式用于布朗尼运动的一类预期变换，该公式将指数级功能作为预期因素。我们的结果统一了早期作品中的现有公式。作为一种应用，我们还考虑了布朗尼运动定律受到相当宽的阶级的积极重量的扰动，并证明其在与扰动相关的预期转变下的不变性。在探索过程中，与指数功能有关的维纳措施的瓦解公式起着关键作用。
In this paper, with the help of a result by Matsumoto--Yor (2000), we prove a Girsanov-type formula for a class of anticipative transforms of Brownian motion which possesses exponential functionals as anticipating factors. Our result unifies existing formulas in earlier works. As an application, we also consider the law of Brownian motion perturbed by a positive weight of a fairly wide class, and prove its invariance under an anticipative transformation associated with the perturbation. In the course of our exploration, a disintegration formula for the Wiener measure related to exponential functionals plays a key role.
