R functions for ‘Exact simulation of Ornstein-
Uhlenbeck processes driven by symmetric -stable
motions’

1 Introduction
Type: R functions for ‘Exact simulation of Ornstein-Uhlenbeck processes driven
by symmetric -stable motions’
Version: 1.0
Date: 2011-2-9
Author: Shibin Zhang
Maintainer: Shibin Zhang <sbzhang@shmtu.edu.cn>
Description: This document provides R functions for the exact simulation
method of Ornstein-Uhlenbeck processes driven by symmetric -stable motions
using the parametrisation described by Zhang and Zhang (2011).
Usage: To use the software, you will need to download the file SOU.R

(SOU.rar) into a
suitable directory on your computer. This contains the functions listed below
and various supporting functions. You should not need to look at the R code
in this file unless you want to see the details of what’s going on.
2 The functions
rS(n,alpha,sigma)
SOU(x=0, lambda=1, alpha=1, sigma=1, T=1, N=100)
The function rS is used to sample n points from the symmetric S (;) distribution
with index of stability  2 (0; 2] and scale parameter  2 (0;1). And the
function rS employs the method in Chambers et al. (1976) and Weron (1995).
The function SOU is the simulator of the O-U process driven by a symmetric
S (1; 0; 0) motion. lambda is the intensity parameter of the O-U process. sigma is
constant parameter multiplied before the background driving term. x is the initial
value of the process at time t0. T is the final time. N is the number of intervals in
which to split [t0,T]. The function employ the method descibed in Zhang and
Zhang (2011).

 

(SOU.rar)

 

References
Chambers, J. M., Mallows, C. L., Stuck, B.W., 1976. A method for simulating
stable random variables. J. Amer. Statist. Assoc. 71, 340-344.
R Development Core Team, 2009. R: A language and environment for statistical
computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-
900051-07-0, URL http://www.R-project.org.
Weron, R., 1996. On the Chambers-Mallows-Stuck method for simulating skewed
stable random variables. Statistics & Probability Letters 28, 165-171.
Zhang S., Zhang X., 2011. Transition law-based least squares estimator for
Ornstein-Uhlenbeck processes driven by -stable motions. submitted.