Geometric Brownian motion with delay : mean square characterisation

Appleby, John A. D. and Mao, Xuerong and Riedle, Markus (2009) Geometric Brownian motion with delay : mean square characterisation. Proceedings of the American Mathematical Society, 137 (1). pp. 339-348. ISSN 0002-9939 (https://doi.org/10.1090/S0002-9939-08-09490-2)

[thumbnail of strathprints014050]
Preview
 Text. Filename: strathprints014050.pdf
Accepted Author Manuscript
License: Creative Commons Attribution-NonCommercial 4.0 logo
Download (507kB)| Preview

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.

ORCID iDs

Appleby, John A. D., Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864 and Riedle, Markus;
CORE (COnnecting REpositories)