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.