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MathGroup Archive 2006

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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65295] Re: How to sample a 2-dim. r.v. with known density function?
  • From: "KvS" <keesvanschaik at gmail.com>
  • Date: Fri, 24 Mar 2006 00:59:59 -0500 (EST)
  • References: <dvrbl7$a1l$1@smc.vnet.net><dvu3id$7vq$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Hi Alan,

thanks for your response but actually you're decribing the situation
where I'm coming from, that is I'm doing some simulation stuff in which
I sample a geom BM the way you suggested. The problem (which was also
mentioned in relevant literature) ias now that with such an approach
calculating the running max gives a very poor result when used to
approximate the first hitting time of a level e.g. One of the reasons
for this is that there are a significant number of paths that actually
do cross the level (in cts. time) but remain below the level at the
discrete time points at which you sample.

That's why I want to switch to sampling not only a new Gaussian at each
discrete time step but sample from the joint distribution of the geom
BM and its running max at the next time step to be able to determine
via the running max if the level was actually crossed in between the
two discrete time points.


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