ABSTRACT

We consider a Feynman-Kac model (1.37) associated with a sequence of Markov transitions Mn and potential functions Gn on some measurable state spaces En. The unnormalized Feynman-Kac measures γn ∈M(En) are given for any fn ∈ Bb(En) by the following formulae

γn(fn) = E

fn(Xn) ∏ 0≤p<n

Gp(Xp)

 = ηn(fn) ∏ 0≤p<n

ηp (Gp)

The product formulae expressing γn in terms of the flow of normalized distributions (ηp)0≤p≤n are proved in (9.3).