Geometric Brownian motion with delay: mean square characterisation

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

Research output: Contribution to journalArticle

10 Citations (Scopus)
10 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)339-348
Number of pages9
JournalProceedings of the American Mathematical Society
Volume137
Issue number1
DOIs
Publication statusPublished - 2009

Keywords

  • geometric Brownian motion
  • mean square characterisation
  • differential equations

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