File:HittingTimes1.png
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Description |
English: Hitting times and stopping times of three samples of brownian motion
Deutsch: Hitting time von drei Sampels der Brownschen Bewegung als Beispiel für eine Stoppzeit.
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Date | |
Source | with the help of GNU R statistics / math software. see the source below |
Author | Thomas Steiner |
Permission (Reusing this file) |
Thomas Steiner put it under the GFDL |
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R-source code:
T=7 N=100000 set.seed(303898) a=0.9 cs=c("orange", "navy", "seagreen4", "grey31") bm1=c(0,cumsum(rnorm(N,mean=0,sd=sqrt(T/N)))) tau1=which(bm1>a)[1] bm1[tau1:(N+1)]=a bm2=c(0,cumsum(rnorm(N,mean=0,sd=sqrt(T/N)))) tau2=which(bm2>a)[1] bm2[tau2:(N+1)]=a bm3=c(0,cumsum(rnorm(N,mean=0,sd=sqrt(T/N)))) tau3=which(bm3>a)[1] bm3[tau3:(N+1)]=a png(filename = "HittingTimes1.png", width=1200, height=900, pointsize = 12) par(bg="gray88") t=seq(0,T,length=N+1) plot(t,bm1,type="l",ylim=range(bm1,bm2,bm3,a*1.2),col=cs[1],lwd=2,ylab="",xlab="Zeit",main="Hitting time von drei Sampels der Brownschen Bewegung als Beispiel für eine Stoppzeit") lines(t,bm2,col=cs[2],lwd=2) lines(t,bm3,col=cs[3],lwd=2) abline(h=a,col=cs[4],lty=1,lwd=3) text(x=tau1*T/N,y=a*1.14, labels = substitute(tau[2]==t1,list(t1=tau1*T/N)),pos=4,col=cs[1],cex=1.5) text(x=tau2*T/N,y=a*1.14, labels = substitute(tau[1]==t2,list(t2=tau2*T/N)),pos=4,col=cs[2],cex=1.5) text(x=T,y=a*1.14, labels = substitute(tau[3]>T,list(T=T)),pos=2,col=cs[3],cex=1.5) dev.off()
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current | 23:03, 7 April 2006 | 1,200 × 900 (17 KB) | Thire (talk | contribs) | ||
22:53, 7 April 2006 | 1,200 × 900 (18 KB) | Thire (talk | contribs) | {{Information| |Description = some stopping times (even hitting times!) of brownian motion |Source = with the help of GNU R statistics / math software. see the source below |Date = 8 Apr. 2006 |Author = Thomas Steiner |Permission = |
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