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How to sample a 2-dim. r.v. with known density function?

• To: mathgroup at smc.vnet.net
• Subject: [mg65247] How to sample a 2-dim. r.v. with known density function?
• From: "KvS" <keesvanschaik at gmail.com>
• Date: Wed, 22 Mar 2006 06:13:37 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

Hi all,

I guess the title explains it already, I have a 2-dim. density function
(the joint density of a geometric Brownian motion with drift and its
running maximum to be more precise, explicit formula can e.g. be found
here: www.maths.ox.ac.uk/~hambly/PDF/O10/lecture15.pdf) and now I would
like to generate random pairs according to this density. I'm not even
sure whether a general method for doing this exists, is anybody
familiar with a method that I can either implement myself in
Mathematica or built-in stuff that can be used to do this?

Lots of thanks in advance,

- Kees