Sharp probability estimates for random walks with barriers
arXiv:math/0610450
Abstract
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.
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