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Science Forum Index » Statistics - Math Forum » Transition density function...
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 Posted: Sat May 10, 2008 7:57 pm |
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Guest
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Hi all,
I need some help in understanding the solution of a problem that I'm
reading. The problem given is that Xt is a standard OU process that is
a stationary Gaussian process with E(Xt) = 0, cov(Xt,Xs) = exp(-(t-s))
for t>s
Solution given is that the pdf of Xs, p(x,s) = (1/sqrt(2*pi))*exp(-
(x^2)/2)
and joint pdf of (Xs, Xt) is
p(x,s;y,t) = (1/sqrt(1-exp(-2(t-s))))*exp(-(y^2+x^2-2xyexp(-(t-s)))/
(2(1-exp(-2(t-s))))
I'm struggling to understand how I could obtained the joint pdf given
above. I guess the solution may have skipped a few steps or perhaps I
can't understand some fundamental relationships in obtaining the
solution. Any help is really appreciated.
Thanks. |
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