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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.

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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}
}

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9 pages