Geometric Brownian motion with delay: mean square characterisation

John A. D. Appleby, Xuerong Mao, Markus Riedle

Research output: Contribution to journalArticle

9 Citations (Scopus)

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 coefficient.
LanguageEnglish
Pages339-348
Number of pages9
JournalProceedings of the American Mathematical Society
Volume137
Issue number1
DOIs
Publication statusPublished - 2009

Fingerprint

Geometric Brownian Motion
Brownian movement
Mean Square
Diffusion Coefficient
Differential equations
Stochastic Functional Differential Equations
Stochastic Equations
Linearly
Asymptotic Behavior
Differential equation
Necessary Conditions
Sufficient Conditions

Keywords

  • geometric Brownian motion
  • mean square characterisation
  • differential equations

Cite this

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

In: Proceedings of the American Mathematical Society, Vol. 137, No. 1, 2009, p. 339-348.

Research output: Contribution to journalArticle

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