Picture of scraped petri dish

Scrape below the surface of Strathprints...

Explore world class Open Access research by researchers at the University of Strathclyde, a leading technological university.

Explore

Geometric Brownian motion with delay: mean square characterisation

Mao, X. and Appleby, J.A.D. and Riedle, M. (2009) Geometric Brownian motion with delay: mean square characterisation. Proceedings of the American Mathematical Society, 137 (1). pp. 339-348. ISSN 0002-9939

[img]
Preview
PDF (strathprints014050.pdf)
strathprints014050.pdf

Download (960kB) | 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.