File:OrnsteinUhlenbeck3.png
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
OrnsteinUhlenbeck3.png (800 × 600 pixels, file size: 42 KB, MIME type: image/png)
File information
Structured data
Captions
DescriptionOrnsteinUhlenbeck3.png |
three sample paths of an Ornstein-Uhlenbeck Process English: three sample paths of different OU-processes with θ=1, μ=1.2, σ=0.3: navy: initial value a=0 (a.s.) |
Date | |
Source | made with the free software R, see the source code at the bottom |
Author | Thomas Steiner |
Permission (Reusing this file) |
Thomas Steiner put it under the GFDL |
Other versions | Image:OrnsteinUhlenbeck.png (replaced because such a filename exists in the german wikipedia) |
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. | ||
| ||
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:
#Orenstein-Uhlenbeck Prozess mit normalverteiltem Anfangswert ou<-function(theta=1, mu=1.2, sigma=0.3, init=c(mu, sigma^2/(2*theta)), from=0, to=2, steps=500*(to-from)) { t<-seq(from,to,length=steps) oup<-rnorm(n=1,mean=init[1],sd=sqrt(init[2])) for (i in (1:(steps-1))) { oup[i+1]=oup[i] + theta*(mu-oup[i])*(to-from)/steps+sigma*rnorm(n=1,mean=0,sd=sqrt(sigma^2*(to-from)/steps)) } return(oup) } cols=c("navy", "darkolivegreen4", "red") t<-seq(0,2,length=1000) set.seed(311051) png(filename="OrnsteinUhlenbeck3.png", width=1200, height=900, pointsize=12) par(bg="lightgrey") matplot(t,ou(init=c(0,0)),type="l", xlab="", ylab="",col=cols[1], lwd=2, ylim=c(0,2)) lines(t,ou(init=c(2,0)),col=cols[2], lwd=2) lines(t,ou(),col=cols[3], lwd=2) title(main="Ornstein - Uhlenbeck", cex.main=2.5) text(x=1.85,y=0,expression(list(theta==1, mu==1.2, sigma == 0.3)) ) text(x=1.55,y=1.75,expression(paste("d",X[t]==theta(mu-X[t]),"dt+",sigma,"d", W[t])),cex=2.5) 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=0.03,y=1.29, expression(paste(X[0], "~N(", mu,",", frac(sigma^2,2*theta), ")") ),col=cols[3]) abline(h=1.2, lty=3, col="grey25") dev.off()
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 03:55, 29 January 2017 | 800 × 600 (42 KB) | Vitez Hirald (talk | contribs) | high contrast | |
22:57, 20 December 2005 | 1,200 × 900 (12 KB) | Thire (talk | contribs) | now the right file?! | ||
15:34, 20 December 2005 | 1,200 × 900 (20 KB) | Thire (talk | contribs) | {{Information| |Description = three sample paths of an Ornstein-Uhlenbeck Process |Source = made with the free software ''R'', see the source code at the bottom |Date = 20 Dec 2005 |Author = Thomas Steiner |Permission = [[:de:Benutz |
You cannot overwrite this file.
File usage on Commons
The following page uses this file:
File usage on other wikis
The following other wikis use this file:
- Usage on de.wikipedia.org
- Usage on de.wikibooks.org
- Usage on fr.wikipedia.org
- Usage on ja.wikipedia.org
- Usage on pt.wikipedia.org
- Usage on sr.wikipedia.org
- Usage on zh.wikipedia.org