Description Usage Format Examples
The dataset contains discretely sampled observations for a simulated stochastic differential equation (SDE) with dynamics:
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
where dW_t
and dB_t
are standard Brownian motions, t
is time and X_0 = 5
, Y_0 = 5
.
1 | data("SDEsim2")
|
A data frame with 801 observations on the following 3 variables.
Xt
Xt trajectory of the diffusion.
Yt
Yt trajectory of the diffusion.
time
Time vector (time[i+1]-time[i] = 1/8
).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 | 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))
|
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