### Abstract

Language | English |
---|---|

Pages | 339-348 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 137 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

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### Keywords

- geometric Brownian motion
- mean square characterisation
- differential equations

### Cite this

*Proceedings of the American Mathematical Society*,

*137*(1), 339-348. https://doi.org/10.1090/S0002-9939-08-09490-2

}

*Proceedings of the American Mathematical Society*, vol. 137, no. 1, pp. 339-348. https://doi.org/10.1090/S0002-9939-08-09490-2

**Geometric Brownian motion with delay : mean square characterisation.** / Appleby, John A. D.; Mao, Xuerong; Riedle, Markus.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Geometric Brownian motion with delay

T2 - Proceedings of the American Mathematical Society

AU - Appleby, John A. D.

AU - Mao, Xuerong

AU - Riedle, Markus

PY - 2009

Y1 - 2009

N2 - 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 coefficient.

AB - 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 coefficient.

KW - geometric Brownian motion

KW - mean square characterisation

KW - differential equations

U2 - 10.1090/S0002-9939-08-09490-2

DO - 10.1090/S0002-9939-08-09490-2

M3 - Article

VL - 137

SP - 339

EP - 348

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 1

ER -