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Geometric Brownian Motion with delay: mean square characterisation

J. A. D. Appleby·M. Riedle
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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.

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J. A. D. Appleby, M. Riedle. 2007-03-28. Geometric Brownian Motion with delay: mean square characterisation. https://arxiv.org/abs/math/0703837

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