File:BrownscheBewegung.png
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DescriptionBrownscheBewegung.png | Algorithmische Konstruktion der Brownschen Bewegung als Summe von normalverteilten Zufallsgrößen |
Date | |
Source | selbst erstellt mit de:GNU R. |
Author | Thomas Steiner |
Permission (Reusing this file) |
Thomas Steiner put it under the GFDL |
Other versions | de:Bild:BrownscheBewegung.png |
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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 |
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This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | |
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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:
set.seed(303898) H=14 #Anzahl der Halbierungsschritte if (exists("B")) { #nach dem ersten Durchlauf als Variable vorhanden mBM=range(B) #max und min der BM, für ylim des plots; } else { mBM=c(-1, 0.8) } B=array(data=0,dim=2) #Startpunkt der Brownschen Bewegung B[2]=rnorm(n=1, mean=0, sd=1) png(filename = "BrownscheBewegung.png", width=1600, height=1200, pointsize=12) par(mfrow = c(2,3), oma = c(0,0,3,0), bg="whitesmoke") plot(x=seq(from=0,to=1,length=2), y=B, type="o", col="red", xlab="Zeit", ylab="BM", ylim=mBM, lwd=3) title(main="i=1, 1 Punkt",cex.main=1.1) for (i in 2:H) { #iteriere über jede Halbierung old=B for (t in 1:2^(i-2)) { #für jeden alten Zeitpunkt gibt es zwei neue (außer dem letzten) B[2*t-1] = old[t] B[2*t] = rnorm(n=1, mean=0.5*(old[t]+old[t+1]), sd=1/(sqrt(2)^i) ) } B[2^(i-1)+1]=old[2^(i-2)+1] # letzter Zeitpunkt if (i<6) {#zeichne nur die ersten 5 plot(x=seq(from=0,to=1,length=2^(i-1)+1),y=B,type="o",col="red",xlab="Zeit",ylab="BM",ylim=mBM,lwd=3) points(x=seq(from=0,to=1,length=2^(i-2)+1),y=old,type="l",col="blue") title(main=paste("i=",i,", ",2^(i-1)+1-1," Punkte",sep=""),cex.main=1.1) } Sys.sleep(0.4) # um es quasi "live" in R zu sehen: "png()" und "dev.off()" auskommentieren! } plot(x=seq(from=0,to=1,length=2^(H-1)+1),y=B,type="l",col="blue",xlab="Zeit",ylab="BM",ylim=mBM,lwd=1) title(main=paste("i=",H,", ",2^(H-1)+1-1," Punkte",sep=""),cex.main=1.1) title(main="Brownsche Brücke - Konstruktion einer Brownsche Bewegung", cex.main=2, outer=TRUE) dev.off()
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current | 11:38, 27 May 2006 | ![]() | 1,600 × 1,200 (23 KB) | Thire (talk | contribs) | {{Information| |Description = Algorithmische Konstruktion der Brownschen Bewegung als Summe von normalverteilten Zufallsgrößen |Source = selbst erstellt mit de:GNU R. |Date = 27 may 2006 |Author = Thomas Steiner |Permission = |
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