21 May 2013, Stone Duality for Markov Processes, Prakash Panangaden

We define Aumann algebras, an algebraic analog of probabilistic modal logic. An Aumann algebra consists of a Boolean algebra with operators modeling probabilistic transitions. We prove a Stone-type duality theorem between countable Aumann algebras and countably-generated continuous-space Markov processes. Our results subsume existing results on completeness of probabilistic modal logics for Markov processes.
(This is joint work with: Dexter Kozen, Kim Larsen and Radu Mardare)