R help - Nov 2007 - simulating a 2-parameter integrated ornstein-uhlenbeck process?

hello everyone,

i'm trying to simulate a 2-parameter integrated ornstein-uhlenbeck (IOU)
process, but i'm not sure exactly where to start (which package, which
function). the motivation is the paper by taylor et. al. (JASA 1994) "a
stochastic model for the analysis of longitudinal aids data." the model
they suggest consists of a combination of fixed and random effects, a stochastic
process, and measurement error.

the 2-parameter IOU process they suggest has cov[W(s), W(t)] =
(sigma^2/(2alpha^3)[2alpha min(s,t)+exp(-alpha* t) +exp(-alpha* s)-1
-exp(alpha*|t-s|)).

any insight into either fitting the model or simulating a 2-parameter IOU
process would be appreciated.

thanks,
farzad





     
____________________________________________________________________________________
Be a better sports nut!  Let your teams follow you 

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You may want to check the package "sde" that can simulate from a
number of
different stochastic differential equations, including the OU process.  

Ravi.



----------------------------------------------------------------------------
-------

Ravi Varadhan, Ph.D.

Assistant Professor, The Center on Aging and Health

Division of Geriatric Medicine and Gerontology 

Johns Hopkins University

Ph: (410) 502-2619

Fax: (410) 614-9625

Email: rvaradhan at jhmi.edu

Webpage:  http://www.jhsph.edu/agingandhealth/People/Faculty/Varadhan.html

 

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-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On
Behalf Of Farzad Noubary
Sent: Wednesday, November 28, 2007 7:58 AM
To: r-help at r-project.org
Subject: [R] simulating a 2-parameter integrated ornstein-uhlenbeck process?

hello everyone,

i'm trying to simulate a 2-parameter integrated ornstein-uhlenbeck (IOU)
process, but i'm not sure exactly where to start (which package, which
function). the motivation is the paper by taylor et. al. (JASA 1994) "a
stochastic model for the analysis of longitudinal aids data." the model
they
suggest consists of a combination of fixed and random effects, a stochastic
process, and measurement error. 

the 2-parameter IOU process they suggest has cov[W(s), W(t)]
(sigma^2/(2alpha^3)[2alpha min(s,t)+exp(-alpha* t) +exp(-alpha* s)-1
-exp(alpha*|t-s|)).

any insight into either fitting the model or simulating a 2-parameter IOU
process would be appreciated.

thanks,
farzad





 
____________________________________________________________________________
________
Be a better sports nut!  Let your teams follow you 

	[[alternative HTML version deleted]]

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