Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Geometric Brownian motion with delay: mean square characterisation


Authors: John A. D. Appleby, Xuerong Mao and Markus Riedle
Journal: Proc. Amer. Math. Soc. 137 (2009), 339-348
MSC (2000): Primary 60H20, 60H10, 34K20, 34K50
Published electronically: April 22, 2008
MathSciNet review: 2439458
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficients depend linearly on the past of the solution, i.e. a linear stochastic functional differential equation. In this work the asymptotic mean square behaviour of a geometric Brownian motion with delay is completely characterised by a sufficient and necessary condition in terms of the drift and diffusion coefficients.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 60H20, 60H10, 34K20, 34K50

Retrieve articles in all journals with MSC (2000): 60H20, 60H10, 34K20, 34K50


Additional Information

John A. D. Appleby
Affiliation: School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland
Email: john.appleby@dcu.ie

Xuerong Mao
Affiliation: Department of Statistical and Modelling Science, Strathclyde University, Glasgow, United Kingdom
Email: xuerong@stams.strath.ac.uk

Markus Riedle
Affiliation: School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
Email: markus.riedle@manchester.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09490-2
PII: S 0002-9939(08)09490-2
Keywords: Stochastic functional differential equations, geometric Brownian motion, mean square stability, renewal equation, variation of constants formula
Received by editor(s): March 23, 2007
Received by editor(s) in revised form: November 15, 2007, and January 11, 2008
Published electronically: April 22, 2008
Additional Notes: The first author was partially funded by an Albert College Fellowship, awarded by Dublin City University’s Research Advisory Panel.
Communicated by: Richard C. Bradley
Article copyright: © Copyright 2008 American Mathematical Society