R functions for Exact simulation of gamma Ornstein-Uhlenbeck processes
 
1 Introduction

Type: R functions for Exact simulation of gamma Ornstein-Uhlenbeck processes
Date: 2010-4-20
Author: Shibin Zhang
Maintainer: Shibin Zhang <sbzhang@shmtu.edu.cn>
Description: This document provides R functions for the exact simulation method
of gamma Ornstein-Uhlenbeck processes.
Usage: To use the software, you will need to download the file gou.R 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

GOU(x=nu/alpha, lambda=1, nu=1, alpha=1, T=1, N=100)
plot.GOU(x=nu/alpha, lambda=1, nu=1, alpha=1, T=1, N=100)

The function GOU is the simulations of the O-U process with
marginal gamma(nu,alpha), where nu is a shape and alpha is a scale. lambda is
the intensity parameter of the O-U process. 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 returns of the function GOU is a N*2 matrix. The first column of the matrix is
the values of the background driving Levy process Z(lambda t) and the second column
is the values of the Gamma O-U process X(t).

The function plot.GOU gives the figures of the Z(lambda t) and X(t).

 

gou.R

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