Geometric Brownian motion with delay: mean square characterisation

Appleby, John; Mao, Xuerong; Riedle, Markus

doi:10.1090/S0002-9939-08-09490-2

Geometric Brownian motion with delay: mean square characterisation
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by John A. D. Appleby, Xuerong Mao and Markus Riedle PDF

Proc. Amer. Math. Soc. 137 (2009), 339-348 Request permission

Abstract:

A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift and diffusion coefficients depend linearly on the past of the solution, i.e. a linear stochastic functional differential equation. In this work the asymptotic mean square behaviour of a geometric Brownian motion with delay is completely characterised by a sufficient and necessary condition in terms of the drift and diffusion coefficients.

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