In this paper we present a stochastic version of Willems’ ideas on Dissipativity and generalize the dissipation inequality to Markov Diffusion Processes.We show the relevance of these ideas by examining the problem of Ergodic Control of partially observed diffusions. A. Rantzer, C.I. Byrnes (Eds.): Directions in Mathematical Systems Theory and Optimization, LNCIS 286, pp. 41-49, 2003. Springer-Verlag Berlin Heidelberg 2003 42 V.S. Borkar, S.K. Mitter 4.