Weighted power variations of iterated Brownian motion
Weighted power variations of iterated Brownian motion
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DOI：
10.1214/ejp.v13-534
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发表时间：
2007-11
影响因子：
1.4
通讯作者：
I. Nourdin;G. Peccati
中科院分区：
文献类型：
--
作者：
I. Nourdin;G. Peccati
我们描述了与迭代布朗运动相关的加权功率变化过程的渐近行为。我们证明了有限维分布意义上的弱收敛结果，并证明了极限物体的定律总是可以用三个独立的布朗运动X， Y和B来表示，以及用局部时间Y来表示。特别是，我们的结果包含了随机场景中Kesten和Spitzer布朗运动的“加权”版本。我们的发现扩展了Khoshnevisan和Lewis（1999）提出的理论，并且应该与Nourdin和Reveillac（2008）最近的结果进行比较，该结果涉及Hurst指数$H=1/4$时分数布朗运动的加权功率变化。
We characterize the asymptotic behaviour of the weighted power variation processes associated with iterated Brownian motion. We prove weak convergence results in the sense of finite dimensional distributions, and show that the laws of the limiting objects can always be expressed in terms of three independent Brownian motions $X, Y$ and $B$, as well as of the local times of $Y$. In particular, our results involve ''weighted'' versions of Kesten and Spitzer's Brownian motion in random scenery. Our findings extend the theory initiated by Khoshnevisan and Lewis (1999), and should be compared with the recent result by Nourdin and Reveillac (2008), concerning the weighted power variations of fractional Brownian motion with Hurst index $H=1/4$.