ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

12. Probability and Statistics

1991 MS Classification: 60G50, 60J15 Siegmund-Schultze, Rainer Level Crossing Probabilities for Random Walks For an arbitrary one-dimensional random walk with independent increments we prove that the probability of crossing a level at a given time n is O(n^{−1/2}). Moment assumptions are not necessary to obtain this upper estimate. As an application, the result is used to prove a conjecture of Mauldin, Monticino and v. Weizsäcker (Adv. Math. 117(2) 1996, 239-252) about transience of directionally reinforced three-dimensional random walks.