File:Cauchy-OU.png
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DescriptionCauchy-OU.png | A cauchy-process (levy-process) and an OU process driven by it. and the median of the invariant distribution |
Date | |
Source | created with GNU R, see source below |
Author | Thomas Steiner |
Permission (Reusing this file) |
Thomas Steiner put it under the CC-by-SA 2.5. |
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R-source Code:
###################################################### ### OU-levy processes ################################ # trajectory of an OU-process, driven by some levy process (bdlp; here cauchy or gamma) ## starting at time t=0 at Z_0=Z0 until time t=T in "steps" equidistant steps; mean reversion "mr" ## parameters of the distribution of the bdlp are stored in param process.ou<-function(param=c(0,1),mr=1,T=1,steps=500,bdlp="cauchy",Z0=0) { dt=T/(steps-1) ou=array(Z0,dim=steps) if (bdlp=="cauchy") { dLt=rcauchy(steps-1, location=param[1], scale=param[2]*dt) } else if (bdlp=="gamma") { dLt=rgamma(n=steps-1, shape=param[1], scale=param[2]*dt) } for (tm in 1:(steps-1)) { ou[tm+1]=ou[tm]-mr*ou[tm]*dt+dLt[tm] } return (list(time=seq(0,T,length=steps),Lt=c(0,cumsum(dLt)),ou=ou)) } set.seed(29011980) time=seq(0,5.7,length=5000)
png("Cauchy-OU.png",width=1200, height=900) par(mfrow=c(2,1)) cou=process.ou(param=c(0,1),mr=1.2,T=max(time),steps=length(time),bdlp="cauchy",Z0=-1.9) plot(cou$time,cou$Lt,type="p",pch=".",main="Cauchy process",col="purple",xlab="",ylab="") plot(cou$time,cou$ou,type="p",pch=".",main="Cauchy-OU process",col="purple",xlab="",ylab="") abline(h=0,lty="dotted",col="darkgrey") #median of limit distribution dev.off()
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current | 15:53, 4 May 2007 | 1,200 × 900 (7 KB) | Thire (talk | contribs) | {{Information |Description = A cauchy-process (levy-process) and an OU process driven by it. and the median of the invariant distribution |Source = created with GNU R, see source below |Date = 4. may 2007 |Author = Thomas Steiner |P |
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