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R-Quelltext:

##SQRT-Diffusion mit normalverteiltem Anfangswert
sdiff<-function(kappa=1, theta=1.2, sigma=0.2, init=c(0, 1), from=0, to=2, steps=500*(to-from)) {
  t<-seq(from,to,length=steps)
  cir<-rnorm(n=1,mean=init[1],sd=sqrt(init[2]))
  for (i in (1:(steps-1))) {
    cir[i 1]=cir[i]   kappa*(theta-cir[i])*(to-from)/steps   sqrt(cir[i])*sigma*rnorm(n=1,mean=0,sd=sqrt((to-from)/steps))
  }
  return(cir)
}

cols=c("navy", "darkolivegreen4", "red")
t<-seq(0,2,length=1000)
set.seed(17091945) 

png(filename="SQRTDiffusion.png", width=1200, height=900, pointsize=12)
par(bg="lightgrey")
matplot(t,sdiff(init=c(0,0)),type="l", xlab="", ylab="",col=cols[1], lwd=2, ylim=c(0,1.55))
lines(t,sdiff(init=c(1.5,0)),col=cols[2], lwd=2)
lines(t,sdiff(),col=cols[3], lwd=2)
title(main="SQRT - Diffusion", cex.main=2.5)
text(x=1.85,y=0,expression(list(kappa==1, theta==1.2, sigma == 0.2)) )
text(x=1.4,y=0.3,expression(paste("d",X[t]==kappa(theta-X[t]),"dt ",sigma,sqrt(X[t]),"d",  W[t])),cex=2.5)
text(x=0,y=0.07, expression(X[0]==0),col=cols[1])
text(x=0,y=1.42, expression(X[0]==2),col=cols[2])
text(x=0.03,y=0.35, expression(paste(X[0], "~N(0,1)") ),col=cols[3])
dev.off()

 

This chart was created with R.