Geometric Brownian Motion with delay: mean square characterisation
Probability
2007-05-23 v1 Dynamical Systems
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 coefficients.
Cite
@article{arxiv.math/0703837,
title = {Geometric Brownian Motion with delay: mean square characterisation},
author = {J. A. D. Appleby and M. Riedle},
journal= {arXiv preprint arXiv:math/0703837},
year = {2007}
}
Comments
9 pages