Picture water droplets

Developing mathematical theories of the physical world: Open Access research on fluid dynamics from Strathclyde

Strathprints makes available Open Access scholarly outputs by Strathclyde's Department of Mathematics & Statistics, where continuum mechanics and industrial mathematics is a specialism. Such research seeks to understand fluid dynamics, among many other related areas such as liquid crystals and droplet evaporation.

The Department of Mathematics & Statistics also demonstrates expertise in population modelling & epidemiology, stochastic analysis, applied analysis and scientific computing. Access world leading mathematical and statistical Open Access research!

Explore all Strathclyde Open Access research...

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

[img]
Preview
Text (strathprints014050)
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.