Moderate deviations for a random walk in random scenery
Moderate deviations for a random walk in random scenery
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DOI：
10.1016/j.spa.2007.11.001
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发表时间：
2006-04
影响因子：
1.4
通讯作者：
K. Fleischmann;Peter Morters;V. Wachtel
中科院分区：
文献类型：
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作者：
K. Fleischmann;Peter Morters;V. Wachtel
我们假设场景变量满足 Cramér 条件，研究了与独立、同分布的随机场景中的随机游走相关的累积场景过程。我们证明了维度 d≥2 的适度偏差原理，涵盖了速率和速度不依赖于场景实际分布的所有情况。对于 d≥4 的情况，我们甚至获得了适度偏差概率的精确渐近，扩展了 Kesten 和 Spitzer 的经典中心极限定理。对于 d≥3，证明中的一个重要因素是随机游走的自相交局部时间的新集中不等式，这是独立的兴趣，而对于 d=2，我们使用最近的自相交局部时间的适度偏差结果，这是 Bass、Chen 和 Rosen 的成果。
We investigate the cumulative scenery process associated with random walks in independent, identically distributed random sceneries under the assumption that the scenery variables satisfy Cramér’s condition. We prove moderate deviation principles in dimensions d≥2, covering all those regimes where rate and speed do not depend on the actual distribution of the scenery. For the case d≥4 we even obtain precise asymptotics for the probability of a moderate deviation, extending a classical central limit theorem of Kesten and Spitzer. For d≥3, an important ingredient in the proofs is the new concentration inequalities for self-intersection local times of random walks, which are of independent interest, whilst for d=2 we use a recent moderate deviation result for self-intersection local times, which is due to Bass, Chen and Rosen.