File:HittingTimes1.png

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

Original file(1,200 × 900 pixels, file size: 17 KB, MIME type: image/png)

Captions

Captions

Add a one-line explanation of what this file represents
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.
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


This graph image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.


It is recommended to name the SVG file “HittingTimes1.svg”—then the template Vector version available (or Vva) does not need the new image name parameter.

(An SVG version should ideally not include the title text, which should be a separate caption as text instead to allow this to be useful in any language).


GNU head 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.
w:en:Creative Commons
attribution share alike
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.

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()
 
This chart was created with R.

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current23:03, 7 April 2006Thumbnail for version as of 23:03, 7 April 20061,200 × 900 (17 KB)Thire (talk | contribs)
22:53, 7 April 2006Thumbnail for version as of 22:53, 7 April 20061,200 × 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 =

File usage on other wikis

The following other wikis use this file: