Reflected Brownian Motion in a Convex Polyhedral Cone: Tail Estimates for the Stationary Distribution

Reflected Brownian Motion in a Convex Polyhedral Cone: Tail Estimates for the Stationary... Consider a multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this distribution at an exponential rate, as time goes to infinity, complementing the results of Dupuis and Williams (Ann Probab 22(2):680–702, 1994) and Atar et al. (Ann Probab 29(2):979–1000, 2001). We also prove that certain exponential moments for this distribution are finite, thus providing a tail estimate for this distribution. Finally, we apply these results to systems of rank-based competing Brownian particles, introduced in Banner et al. (Ann Appl Probab 15(4):2296–2330, 2005). http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Theoretical Probability Springer Journals

Reflected Brownian Motion in a Convex Polyhedral Cone: Tail Estimates for the Stationary Distribution

Loading next page...
 
/lp/springer_journal/reflected-brownian-motion-in-a-convex-polyhedral-cone-tail-estimates-aJFtB2bCb0
Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Mathematics; Probability Theory and Stochastic Processes; Statistics, general
ISSN
0894-9840
eISSN
1572-9230
D.O.I.
10.1007/s10959-016-0674-8
Publisher site
See Article on Publisher Site

Abstract

Consider a multidimensional obliquely reflected Brownian motion in the positive orthant, or, more generally, in a convex polyhedral cone. We find sufficient conditions for existence of a stationary distribution and convergence to this distribution at an exponential rate, as time goes to infinity, complementing the results of Dupuis and Williams (Ann Probab 22(2):680–702, 1994) and Atar et al. (Ann Probab 29(2):979–1000, 2001). We also prove that certain exponential moments for this distribution are finite, thus providing a tail estimate for this distribution. Finally, we apply these results to systems of rank-based competing Brownian particles, introduced in Banner et al. (Ann Appl Probab 15(4):2296–2330, 2005).

Journal

Journal of Theoretical ProbabilitySpringer Journals

Published: Apr 12, 2016

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off