带障碍随机游走的精确概率估计
概率论
2009-06-18 v4
摘要
对于给定的终点 x，我们对实数轴上 n 步随机游走避开半直线 [y,∞) 的概率给出了精确的、一致的估计。这些估计对一般的连续或格点分布均成立，只需其四阶矩有限。
引用
@article{arxiv.math/0610450,
title = {Sharp probability estimates for random walks with barriers},
author = {Kevin Ford},
journal= {arXiv preprint arXiv:math/0610450},
year = {2009}
}
备注
v3. 12 pages. Significantly shorter proofs and stronger results in section 6. Lemma 7.1 now proved assuming absolute third moment. A more general version of Theorem 1 given, where the variables are assumed to have a u-th moment for any real u>3. Strengthened Corollary 2. Two references added