You'll have to give me your email address. I'll be happy to send you that article.
[ QUOTE ]
can you recommend a good article on brownian motion -- it's a been a while since i studied it and i no longer have my books.
[/ QUOTE ]
My standard reference is "Brownian Motion and Stochastic Caluclus" by Karatzas and Shreve. I learned out of that book originally and, interestingly, it's the first listing in Google Scholar when you search for "brownian motion." I don't know of any article off-hand, but there are some lecture notes
here that look nice. She talks about the Invariance Principle of p.27 of the lectures 5-8 pdf and lecture 9 is nice as well. There are probably a lot of other course notes out there waiting to be googled, especially in finance.
[ QUOTE ]
Finally, how do you approach the problem in the 25BB case, where convergence theorems are no longer accurate. Do we need to approximate the underlying per hand distribution, perhaps using PT data, and then run a simulation?
[/ QUOTE ]
I somehow doubt one could get an accurate enough approximation to the underlying per hand distribution. Aren't 25BB downswings fairly common? It sure feels like they are. I have about 20K hands in my db. I'd have to check, but there must be many 25BB downswings. I think I would just measure the time between these downswings and take these times to be independent realizations of T. (I never tilt, of course. [img]/images/graemlins/smile.gif[/img]) I don't know what kind of analysis you could do with that or how accurate it would be. I suppose that depends on how many of these swings you've had.
If you get any data on this, let me know. I'm curious.