A Simulated Diffusion with Sinusoidal Drift and State-Dependant Diffusion Coefficient.

Description

The dataset contains discretely sampled observations for a simulated stochastic differential equation (SDE) with dynamics:

dX_t = 2(5+3sin(0.25pi t)-X_t)dt+0.5sqrt(X_t)dW_t

where dW_t is standard Brownian motion, t is time and X_0 = 7.

Usage

data(SDEsim1)

Format

A data frame with 401 observations with the following variables:

1. Xt : A numeric vector of simulated observations.

2. time : A numeric vector of time nodes at which Xt was observed (time[i+1]-time[i] = 1/4).

Details

The process was simulated by numerically solving the SDE using a Euler-Maruyama scheme with stepsize = 1/2000. Subsequently each 200-th observation was recorded in order to construct the resulting time series.

Author(s)

Etienne A.D. Pienaar: etiannead@gmail.com

References

Updates available on GitHub at https://github.com/eta21.

Examples

 data(SDEsim1)
 attach(SDEsim1)
 par(mfrow=c(1,1))
 expr1=expression(dX[t]==2*(5+3*sin(0.5*pi*t)-X[t])*dt+0.5*sqrt(X[t])*dW[t])
 plot(Xt~time,type='l',col='blue',xlab='Time (t)',ylab=expression(X[t]),main=expr1)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(DiffusionRgqd)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/DiffusionRgqd/SDEsim1.Rd_%03d_medium.png", width=480, height=480)
> ### Name: SDEsim1
> ### Title: A Simulated Diffusion with Sinusoidal Drift and State-Dependant
> ###   Diffusion Coefficient.
> ### Aliases: SDEsim1
> ### Keywords: datasets
> 
> ### ** Examples
> 
>  data(SDEsim1)
>  attach(SDEsim1)
>  par(mfrow=c(1,1))
>  expr1=expression(dX[t]==2*(5+3*sin(0.5*pi*t)-X[t])*dt+0.5*sqrt(X[t])*dW[t])
>  plot(Xt~time,type='l',col='blue',xlab='Time (t)',ylab=expression(X[t]),main=expr1)
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>