On the trivariate joint distribution of Brownian motion and its maximum and minimum

ByoungSeon Choi and JeongHo Roh

Statistics & Probability Letters, 2013, vol. 83, issue 4, 1046-1053

Abstract: The trivariate joint probability density function of Brownian motion and its maximum and minimum can be expressed as an infinite series of normal probability density functions. In this letter, we show that the infinite series converges uniformly, and satisfies the Fokker–Planck equation. Also, we express it as a product form using Jacobi’s triple product identity, and present some error bounds of a finite series approximation of the infinite series.

Keywords: Brownian motion; Maximum and minimum; Joint probability distribution; Jacobi’s triple product identity (search for similar items in EconPapers)
Date: 2013
References: View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715212004749
Full text for ScienceDirect subscribers only

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:eee:stapro:v:83:y:2013:i:4:p:1046-1053

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2012.12.015

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().