Statistics Seminars: Stationary flows and uniqueness of invariant measures
7 March 2007 14:00 in CM221
We consider a flow on a probability space which preserves the underlying (probability) measure and derive a relation between (i) the mean number of visits to set A, by the trajectory of a point, until the first time another set B is visited with (ii) the measure of A on the event that the first time that the set B is visited in backwards time. It turns out that this relation generalises a classical formula due to Mark Kac and reduces, in special cases, to the so-called Neveu's exchange formula between Palm probabilities (a simple relation in discrete time). It gives a new method for proving uniqueness of invariant measures in stochastic models such as Harris ergodic Markov chains in discrete time and general state space.
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