File:SQRTDiffusion4.png

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

	This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
	You are free: to share – to copy, distribute and transmit the work to remix – to adapt the work Under the following conditions: attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use. share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
	This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue

R-Quelltext:

##SQRT-Diffusion mit normalverteiltem Anfangswert
sdiff<-function(kappa=5, theta=0.6, sigma=0.2, init=c(1, 1), from=0, to=1.5, steps=1000*(to-from),  bm=rnorm(n=steps-1,mean=0,sd=sqrt((to-from)/steps))) {
  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*bm[i]
  }
  return(cir)
}

cols=c("navy", "darkolivegreen4", "red")
set.seed(290184)

kappa=5
theta=0.6
sigma=0.2
from=0
to=1.5
steps=1000*(to-from)
w1=rnorm(n=steps-1,mean=0,sd=sqrt((to-from)/steps))
w2=rnorm(n=steps-1,mean=0,sd=sqrt((to-from)/steps))
w3=rnorm(n=steps-1,mean=0,sd=sqrt((to-from)/steps))
init=c(rnorm(1,1,1),0)
t<-seq(from,to,length=steps)

png(filename="SQRTDiffusion4.png", width=1200, height=900, pointsize=12)
par(bg="lightgrey", mfrow=c(2,2), oma=c(0,0,3,0))

matplot(t,sdiff(init=c(0,0), bm=w1),type="l", xlab="", ylab="",col=cols[1], lwd=2, ylim=c(0,2))
lines(t,sdiff(init=c(2,0), bm=w2), col=cols[2], lwd=2)
lines(t,sdiff(init=init, bm=w3), col=cols[3], lwd=2)
text(x=1.35,y=1.9,expression(list(kappa==1, theta==1.2, sigma == 0.3)), cex=1.4 )
text(x=0,y=0.07, expression(X[0]==0),col=cols[1])
text(x=0,y=1.92, expression(X[0]==2),col=cols[2])
text(x=0,y=init[1]*1.08, expression(paste(X[0], "~N(1,1)") ),col=cols[3])

matplot(t,sdiff(theta=1.4, init=c(0,0), bm=w1),type="l", xlab="", ylab="",col=cols[1], lwd=2,   ylim=c(0,2))
lines(t,sdiff(theta=1.4, init=c(2,0), bm=w2),col=cols[2], lwd=2)
lines(t,sdiff(theta=1.4, init=init, bm=w3),col=cols[3], lwd=2)
title(main=expression(theta==1.4))

matplot(t,sdiff(sigma=0.4, init=c(0,0), bm=w1),type="l", xlab="", ylab="",col=cols[1], lwd=2, ylim=c(0,2))
lines(t,sdiff(sigma=0.4, init=c(2,0), bm=w2),col=cols[2], lwd=2)
lines(t,sdiff(sigma=0.4, init=init, bm=w3),col=cols[3], lwd=2)
title(main=expression(sigma==0.4))

matplot(t,sdiff(theta=1, kappa=50, init=c(0,0), bm=w1),type="l", xlab="", ylab="",col=cols[1],  lwd=2, ylim=c(0,2))
lines(t,sdiff(theta=1, kappa=50, init=c(2,0), bm=w2),col=cols[2], lwd=2)
lines(t,sdiff(theta=1, kappa=50, init=init, bm=w3),col=cols[3], lwd=2)
title(main=expression(list(theta==1, kappa==50)))

title(main=expression(paste("d",X[t]==kappa(theta-X[t]),"dt+",sigma,sqrt(X[t]),"d", W[t])), cex.main=2.5, outer=TRUE)

dev.off()

 

This chart was created with R.