From: jmb184@frontiernet.net (John Bailey)
Subject: Re: Decomposing a probability density function
Date: Sat, 05 Feb 2000 13:32:45 GMT
Newsgroups: sci.stat.math,sci.math,comp.soft-sys.matlab
Summary: Black-Scholes equation (time varying variance in financial models)

On Fri, 04 Feb 2000 18:28:20 +0100, Alois Schloegl
<schloegl@dpmi.tu-graz.ac.at> wrote:

>Is there any method or algorithm for decomposing a given probability
>density function  into a sum (or product) of gaussian distributions?
>
>given: any histogram H(x)
>
>   p(x,i) is a normal distributed probability density function of x with
>mean mu(i) and variance sigma(i)^2.
>
>    H'(x) = sum (N(i)*p(x,i)) i=1..M
Your problem is close to the problem of handling time varying variance
in financial models--eg Black-Scholes.
A web search with the phrase stochastic volatility yields a lot of
material on this subject:
The document at:
ftp://ftp.cirano.umontreal.ca/pub/publication/95s-49.pdf.zip
may be a bit of overkill, but if your interests are financial, you may
find it stimulating.

John