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Geometric Brownian motion with delay: mean square characterisation
Author(s):
John
A. D.
Appleby;
Xuerong
Mao;
Markus
Riedle
Journal:
Proc. Amer. Math. Soc.
137
(2009),
339-348.
MSC (2000):
Primary 60H20, 60H10, 34K20, 34K50
Posted:
April 22, 2008
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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.
References:
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Additional Information:
John
A. D.
Appleby
Affiliation:
School of Mathematical Sciences, Dublin City University, Dublin 9, Ireland
Email:
john.appleby@dcu.ie
Xuerong
Mao
Affiliation:
Department of Statistical and Modelling Science, Strathclyde University, Glasgow, United Kingdom
Email:
xuerong@stams.strath.ac.uk
Markus
Riedle
Affiliation:
School of Mathematics, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
Email:
markus.riedle@manchester.ac.uk
DOI:
10.1090/S0002-9939-08-09490-2
PII:
S 0002-9939(08)09490-2
Keywords:
Stochastic functional differential equations,
geometric Brownian motion,
mean square stability,
renewal equation,
variation of constants formula
Received by editor(s):
March 23, 2007,
Received by editor(s) in revised form:
November 15, 2007, and January 11, 2008
Posted:
April 22, 2008
Additional Notes:
The first author was partially funded by an Albert College Fellowship, awarded by Dublin City University's Research Advisory Panel.
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2008,
American Mathematical Society
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