Probability transition density -- just need a name

I have a very simple question.

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!
alan



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