Thank you, Alek! The shape is indeed very similar, the main difference being the fact that the noise is taking only values. But the spirit is indeed the same.I have actually wondered more generally about a possible link between recurrence for discrete and continuous random walks…

]]>(with a 2-lines rigorous proof)

]]>http://www.artofproblemsolving.com/Forum/viewtopic.php?uid=96&f=498&t=351254&unwatch=topic

(The one considered in the link is more or less the square of the one considered in this post.)

]]>I have no deep intuition about continuous time processes, but the fact is that the discretised versions do not always enjoy the same properties as their continuous relative. Take, e.g., the Langevin diffusion (which is recurrent) and the Langevin “random walk” (which may be transient)…

]]>**Alek: ** I have had email exchanges with Randal Douc and Arnaud Guillin about this point… My understanding of the behaviour of the null recurrent random walk is that it visits arbitrarily far regions with a positive probability and that it takes on average an infinite time for the random walk to come back near zero. So it does not almost surely go to infinity (which would violate the null recurrence property). However, if we consider the chain itself, its dynamics imply that once it reaches infinity, its variance gets to zero and therefore it remains stuck there. I realise this is not a bullet-proof argument, but it suffices to convince me of the transience of the chain…

For example with has a square that is bounded below by a null recurrent process, but does not tend to infinity almost surely, isn’t it ?

]]>thanks a lot for the code.

I’m new to R and these kind of examples are all very enlightening for me.

Regards,

Ruben ]]>

Thanks for the comment: I use

*H=25
boxplot(as.data.frame(t(abs(resu))),col="wheat3", names=as.character(1:H),borders=FALSE,outline=FALSE,xlab=expression(log[2](T)),ylab="",ylim=c(0,quantile(resu,.95))*

to get a reasonable range for the boxes [ylim] and the numbers at the bottom [names=]

I’d like to replicate your results using R 2.11.0 on Leopard but unfortunately the graph doesn’t match: the boxes are much smaller and the X-axis shows V1…V24 instead of just the numbers.

Any idea how I could fix that?

Many thanks in advance,

Ruben ]]>