Large and moderate deviations for intersection local times
Large and moderate deviations for intersection local times
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DOI：
10.1007/s00440-003-0298-7
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发表时间：
2004-02
影响因子：
2
通讯作者：
Xia Chen;Wenbo V. Li
中科院分区：
文献类型：
--
作者：
Xia Chen;Wenbo V. Li
研究了对称随机游动的独立布朗局部时和独立局部时所产生的相交局部时的大偏差和中等偏差。我们的结果推广了Mansmann（1991）关于布朗局部时L2-范数的大偏差原理，并与Csörgö，Shi和Yor（1991）关于布朗桥自相交局部时的大偏差原理一致.我们的方法依赖于布朗占据时的Feynman-Kac型大偏差，Donsker-Varadhan（1975）和Mansmann（1991）的某些局部化技术，以及在Banach空间中沿着概率线发展的一些一般方法。在随机游动的情况下，我们的处理也涉及到重标度，谱表示和不变性原理。作为偏差结果的一个应用，给出了相交局部时的重对数律。
We study the large and moderate deviations for intersection local times generated by, respectively, independent Brownian local times and independent local times of symmetric random walks. Our result in the Brownian case generalizes the large deviation principle achieved in Mansmann (1991) for theL2-norm of Brownian local times, and coincides with the large deviation obtained by Csörgö, Shi and Yor (1991) for self intersection local times of Brownian bridges. Our approach relies on a Feynman-Kac type large deviation for Brownian occupation time, certain localization techniques from Donsker-Varadhan (1975) and Mansmann (1991), and some general methods developed along the line of probability in Banach space. Our treatment in the case of random walks also involves rescaling, spectral representation and invariance principle. The law of the iterated logarithm for intersection local times is given as an application of our deviation results.