I am working through an already not so easy to find paper from the 70s, which in turn uses an even older result that i can not find at all. Im refering to http://iopscience.iop.org/0305-4470/24/17/010, unfortunately not freely availible as far as i know. The result seems like it might be generally known for people working in stochastic equations, maybe under another name. Equation (6) They refer to it as Klyatski-Tatarski Formula and it looks like this: . $$ \langle z(t) R[z] \rangle_{z}=\nu \langle \xi \rangle + \nu \int_{-\infty}^{\infty} d(\xi)P(\xi) \int_{0}^{\xi} d\nu \langle \exp[\eta\frac{\delta}{\delta z(t)}]R[z] \rangle_{z}, $$
where z(t) describes an Poisson Process, $\langle .\rangle_{z}$ the average over that process, z(t) involves Random Variables §\xi_{i}§ with mean $\langle \xi \rangle$, $\nu$ is the mean number of events during the Poisson process.
Does anyone know that result and point me to a link where i can see it proven, or alternatively is it obvious for anyone who could give me some intuition why it holds?