## 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 |
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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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