2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126530A 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.9 pagesProbabilityDynamical Systems60H20; 60H10; 34K20; 34K50text