Re: Probability transition density -- just need a name


"Dave Elliott" <delliott@xxxxxxx> wrote in message
news:dlvtch$4a1$1@xxxxxxxxxxxxxxxxxxx
>I would say it's the transient term.
>
> [Moderator's Note: The question was as follows:
>
> Suppose we have a stationary Markov process X(t) where X(0) = x,
> with a transition density p(t,x,y)dy = P(X(t) in dy).
>
> As t -> infinity, assume p tends to a stationary (invariant)
> measure f(y). We can always write p(t,x,y) = f(y) + g(t,x,y),
> and this occurs naturally in eigenfunction expansions.
>
> What is a standard name for g( ), if any?
> ]


Thanks, Dave, that sounds a little better than what I
was thinking ("the dynamic term").

Here's a second nomenclature question for you or the group.

With the above notation, f(x) p(t,x,y) is a bivariate
probability density in (x,y) -- call it G(t,x,y).
It measures the joint probability density to start from x
(with a draw from the stationary measure f(x)),
and ending at y after time t.

What's a good (or standard) name for G( )?

regards,
alan


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