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)

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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 |
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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 |

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