2008.1: Geometric Brownian Motion with delay: mean square characterisation
2008.1: J.A.D. Appleby, X. Mao and M. Riedle (2007) Geometric Brownian Motion with delay: mean square characterisation. Proceedings of the AMS. ISSN 0002-9939
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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 2000 > 60 Probability theory and stochastic processes |
| MIMS number: | 2008.1 |
| Deposited By: | Dr Markus Riedle |
| Deposited On: | 11 January 2008 |
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