File:BrownBewKonvergenz.png
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DescriptionBrownBewKonvergenz.png |
Deutsch: Konvergenz eines Prozesses gegen eine Brownsche Bewegung durch Halbierung der Zeitintervalle |
Date | |
Source | Own work |
Author | Thomas Steiner |
Source code (R) InfoField | set.seed(9826064)
H=10 #Anzahl der Halbierungsschritte
c=rainbow(H)
B=0 #Startpunkt der Brownschen Bewegung
B[2]=0+rnorm(n=1,mean=0,sd=2^(1/2*(H-1)))
png(filename = "BrownBewKonvergenz.png", width = 1300, height = 900, pointsize = 12)
plot(x=seq(from=0,to=2^(H-1)+1,length=2),y=B,type="l",col=c[1],xlab="Zeit",ylim=c(-25,25))
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] =old[t]+rnorm(n=1,mean=0,sd=2^(1/2*(H-i)))
}
B[2^(i-1)+1]=old[2^(i-2)+1] # letzter Zeitpunkt
lines(x=seq(from=0,to=2^(H-1)+1,length=2^(i-1)+1),y=B,col=c[i])
Sys.sleep(1.4) # um es quasi "live" in R zu sehen
}
lines(x=seq(from=0,to=2^(H-1)+1,length=2^(H-1)+1),y=B, type="l",lwd=2)
title(main="Konvergenz eines Prozesses gegen eine Brownsche Bewegung",cex.main=2)
dev.off()
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Thomas Steiner, the copyright holder of this work, hereby publishes it under the following license:
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. | ||
Attribution: Thomas Steiner | ||
| ||
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 |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 09:30, 24 March 2005 | 1,300 × 900 (27 KB) | Thire (talk | contribs) | *Beschreibung: Konvergenz eines Prozesses gegen eine Brownsche Bewegung durch halbierung der Zeitintervalle *Quelle: selbst erstellt mit GNU R, Quelltext siehe unten *Fotograf oder Zeichner: Thomas Steiner {{Bild-GFDL}} |
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