Path collapse for multidimensional Brownian motion with rebirth

Ilie Grigorescu and Min Kang

Statistics & Probability Letters, 2004, vol. 70, issue 3, 199-209

Abstract: In a bounded open region of the d-dimensional Euclidean space we consider a Brownian motion which is reborn at a fixed interior point as soon as it reaches the boundary. It was shown that in dimension one coupled paths starting at different points but driven by the same Brownian motion either collapse with probability one or never meet. In higher dimensions, for convex or polyhedral regions, the paths with positive probability of collapse differ at start by a vector from a set of codimension one. The problem can be interpreted in terms of the long term mixing properties of the payoff of a portfolio of knock-out barrier options in derivatives markets.

Keywords: Absorbing; Brownian; motion; Harmonic; measure; Collapsing; paths; Barrier; options (search for similar items in EconPapers)
Date: 2004
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(04)00257-3
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:70:y:2004:i:3:p:199-209

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

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 ().