Appleby, J.A.D. and Mao, X. and Riedle, M. (2007) Geometric Brownian Motion with delay: mean square characterisation. Proceedings of the AMS. ISSN 0002-9939 (In Press)
![[thumbnail of geo_brown_SFDE-2.pdf]](https://eprints.maths.manchester.ac.uk/style/images/fileicons/application_pdf.png) |
PDF
geo_brown_SFDE-2.pdf Download (171kB) |
Official URL: http://www.ams.org/proc/
Abstract
A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional differential equation. In this work the asymptotic behavior in mean square of a geometric Brownian motion with delay is completely characterized by a sufficient and necessary condition in terms of the drift and diffusion coefficients.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | stochastic functional differential equations, geometric Brownian motion, means square stability, renewal equation, variation of constants formula |
| Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes |
| Depositing User: | Dr Markus Riedle |
| Date Deposited: | 11 Jan 2008 |
| Last Modified: | 20 Oct 2017 14:12 |
| URI: | https://eprints.maths.manchester.ac.uk/id/eprint/1009 |
Actions (login required)
 |
View Item |