Geometric Brownian motion with delay: mean square characterisation
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- by John A. D. Appleby, Xuerong Mao and Markus Riedle PDF
- Proc. Amer. Math. Soc. 137 (2009), 339-348 Request permission
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
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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
- MR Author ID: 199088
- ORCID: 0000-0002-6768-9864
- 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
- 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
- © Copyright 2008 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 339-348
- MSC (2000): Primary 60H20, 60H10, 34K20, 34K50
- DOI: https://doi.org/10.1090/S0002-9939-08-09490-2
- MathSciNet review: 2439458