DiffusionRgqd (version 0.1.1)

SDEsim2: A Simulated Non-Linear Bivariate Diffusion

Description

The dataset contains discretely sampled observations for a simulated stochastic differential equation (SDE) with dynamics: html{ {$$dX_t = 2.0(Y_t-X_t)dt+0.3sqrt(X_tY_t)dW_t$$} {$$dY_t = 1.0(5-Y_t)dt+0.5sqrt(Y_t)dB_t$$} } latex{ {$$dX_t = 2.0(Y_t-X_t)dt+0.3\sqrt{X_tY_t}dW_t$$} {$$dY_t = 1.0(5-Y_t)dt+0.5\sqrt{Y_t}dB_t$$} } where dW_t and dB_t are standard Brownian motions, t is time and X_0 = 5, Y_0 = 5.

Usage

data("SDEsim2")

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(SDEsim2)
  data(SDEsim2)
  attach(SDEsim2)
  # Have a look at the time series:
  plot(Xt~time,type='l',col='blue',ylim=c(2,10),main='Simulated Data',xlab='Time (t)',ylab='State',
       axes=FALSE)
  lines(Yt~time,col='red')
  expr1=expression(dX[t]==2(Y[t]-X[t])*dt+0.3*sqrt(X[t]*Y[t])*dW[t])
  expr2=expression(dX[t]==(5-Y[t])*dt+0.5*sqrt(Y[t])*dB[t])
  text(50,9,expr1)
  text(50,8.5,expr2)
  axis(1,seq(0,100,5))
  axis(1,seq(0,100,5/10),tcl=-0.2,labels=NA)
  axis(2,seq(0,20,2))