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Summary: Geometric Brownian Motion with delay: mean
square characterisation
J.A.D. Appleby, X Mao and M Riedle
November 2007
MIMS EPrint: 2008.1
Manchester Institute for Mathematical Sciences
School of Mathematics
The University of Manchester
Reports available from: http://www.manchester.ac.uk/mims/eprints
And by contacting: The MIMS Secretary
School of Mathematics
The University of Manchester
Manchester, M13 9PL, UK
ISSN 1749-9097
GEOMETRIC BROWNIAN MOTION WITH DELAY:
MEAN SQUARE CHARACTERISATION
JOHN A. D. APPLEBY, XUERONG MAO, AND MARKUS RIEDLE
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
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