A Note on Erdös and Kac’s Identity: Boundary Crossing Probabilities of Brownian Motion Over Constant Boundaries

Tung-Lung Wu ()
Additional contact information
Tung-Lung Wu: Mississippi State University

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 1, 161-171

Abstract: Abstract The finite Markov chain imbedding technique is an emerging approach for calculating boundary crossing probabilities for high-dimensional Brownian motion and certain one-dimensional diffusion processes. In 1996, Erdös and Kac produced an infinite series for the crossing probability of Brownian motion over a two-sided constant boundary. We derive this classic result based on a unified formula from the finite Markov chain imbedding technique. Also, an eigenvalues-and-eigenvectors approximation is given for fast computation. The main purpose of this paper is to show the versatility of the finite Markov chain imbedding technique.

Keywords: Boudnary crossing probabilities; Brownian motion; Finite Markov chain imbedding; Random walks; Erdös and Kac’s identity; 60J22; 37A50 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-018-9686-4 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:metcap:v:22:y:2020:i:1:d:10.1007_s11009-018-9686-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-018-9686-4

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().