DiffusionRgqd (version 0.1.1)

SDEsim4: A Simulated Non-Linear Bivariate Diffusion With Time-Inhomogeneous Coefficients

Description

The dataset contains discretely sampled observations for a simulated stochastic differential equation (SDE) with dynamics: html{ {$$dX_t = (1.0(7.5-X_t)+1.5Y_t)dt+0.5sqrt(X_tY_t)dW_t$$} {$$dY_t = (1.5(5-Y_t)+3sin(0.25 pi t ))dt+0.25sqrt(Y_t)dB_t$$} } latex{ {$$dX_t = (1.0(7.5-X_t)+1.5Y_t)dt+0.5\sqrt{X_tY_t}dW_t$$} {$$dY_t = (1.5(5-Y_t)+3\sin(0.25 \pi t ))dt+0.25\sqrt{Y_t}dB_t$$} } where dW_t and dB_t are standard Brownian motions, t is time and X_0 = 10, Y_0 = 5.

Usage

data("SDEsim4")

Details

For a full analysis of this dataset check out Example 7.5 in the example scripts at https://github.com/eta21/DiffusionRgqd-Downloads.

Examples

data(SDEsim4)
data(SDEsim4)
attach(SDEsim4)
# Have a look at the time series:
plot(Xt~time,type='l',col='blue',ylim=c(0,25),main='Simulated Data',
xlab='Time (t)',ylab='State',axes=FALSE)
lines(Yt~time,col='red')
axis(1,seq(0,100,5))
axis(1,seq(0,100,5/10),tcl=-0.2,labels=NA)
axis(2,seq(0,25,2))
axis(2,seq(0,25,2/10),tcl=-0.2,labels=NA)