Geometric Brownian Motion with delay: mean square characterisation

Details Geometric Brownian Motion with delay: mean square characterisation Geometric Brownian Motion with delay: mean square characterisation

2007-03-28

arxiv.org/abs/math/0703837v1

Mathematics

Probability

9 pages

Scientific paper

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.

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