Some Absolute Continuity Relationships for Certain Anticipative Transformations of Geometric Brownian Motions
Some Absolute Continuity Relationships for Certain Anticipative Transformations of Geometric Brownian Motions
复制标题
几何布朗运动某些预期变换的一些绝对连续关系
DOI：
10.2977/prims/1145477226
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发表时间：
2001
影响因子：
1.2
通讯作者：
M. Yor
中科院分区：
文献类型：
--
作者：
C. Donati;H. Matsumoto;M. Yor
我们通过涉及 e (μ) 及其二次变分 {<e>t, t 0} 的某些变换 Tα 来展示几何布朗运动 e = {et , t 0} 的概率定律及其图像之间的绝对连续性关系。这些结果源自我们之前关于广义 Dufresne 恒等式和 Pitman 2M −X 定理 X（具有恒定漂移 μ 的布朗运动及其单边上界 M ）的指数型扩展的结果，并且与我们之前的结果密切相关。然后，这些绝对连续性结果被证明是 Ramer-Kusuoka 对维纳空间非线性变换和 Buckdahn-Follmer 对某些具有预期漂移的随机微分方程的解的特殊情况。
We present some absolute continuity relationships between the probability laws of a geometric Brownian motion e = {e t , t 0} and its images by certain transforms Tα involving e (μ) and its quadratic variation {〈e〉t, t 0}. These results are derived from, and shown to be closely related to, our previous results about the generalized Dufresne’s identity and the exponential type extensions of Pitman’s 2M −X theorem for X, a Brownian motion with constant drift μ, and its one-sided supremum M . These absolute continuity results are then shown to be particular cases of those by Ramer–Kusuoka for non-linear transformations of the Wiener space and by Buckdahn–Follmer for solutions of certain stochastic differential equations with anticipative drifts.
影响因子：
4
作者：
D. Nualart
通讯作者：
D. Nualart