In this paper, a single product continuous time stochastic inventory model for deteriorating items, driven by a. conditional Poisson process, is suggested. It is assumed the process Ztmodulating the jump intensities of the Poisson process is a Markov chain. By observing the history of the inventory level, a finite dimensional filter for the conditional distribution of Ztis found. Further filters are found when the conditional Poisson process is replaced by an integer–valued random measure with predictable compensator depending on a right–constant sample paths process yt