Random Walks Crossing High Level Curved Boundaries

Harry Kesten and R. A. Maller

Journal of Theoretical Probability, 1998, vol. 11, issue 4, 1019-1074

Abstract: Abstract Let }S n} be a random walk, generated by i.i.d. increments X i which drifts weakly to ∞ in the sense that $$S_n \xrightarrow{P}\infty$$ as n→ ∞. Suppose k≥0, k≠1, and E|X 1|1k = ∞ if k>1. Then we show that the probability that S. crosses the curve n↦an K before it crosses the curve n ↦ −an k tends to 1 as a → ∞. This intuitively plausible result is not true for k = 1, however, and for 1/2

Keywords: Random walks; first passage times; boundary crossing probabilities; sequential analysis (search for similar items in EconPapers)
Date: 1998
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://link.springer.com/10.1023/A:1022621016708 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:11:y:1998:i:4:d:10.1023_a:1022621016708

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1023/A:1022621016708

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().