Sharp probability estimates for random walks with barriers
概率论
2009-06-18 v4
摘要
We give sharp, uniform estimates for the probability that a random walk of n steps on the reals avoids a half-line [y,infinity) given that it ends at the point x. The estimates hold for general continuous or lattice distributions provided the 4th moment is finite.
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