Description Usage Format Examples
The dataset contains discretely sampled observations for a simulated stochastic differential equation (SDE) with dynamics:
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
where dW_t
and dB_t
are standard Brownian motions, t
is time and X_0 = 10
, Y_0 = 5
.
1 | data("SDEsim4")
|
A data frame with 401 observations on the following 3 variables.
Xt
Xt trajectory of the diffusion.
Yt
Yt trajectory of the diffusion.
time
Time vector.
1 2 3 4 5 6 7 8 9 10 | 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)
|
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