1:00 pm Friday, February 21, 2014
Jr. Probability: Palm Probabilities and Point-Shifts by Antonio Sodre in RLM 8.136
Palm probability is a key concept in the theory of point process: it can be seen as the conditional probability of the point process given that there is a point at the origin. I will go through Matthes construction of this object, starting from first principles. On the other hand, a point-shift is a deterministic mapping that determines a rule to move from point to point given a realization of a point process. For example, when d=1, "move to the closest point to your right" is a point-shift. In the 60's, Mecke connected these two concepts: if a point process is stationary and simple, and is a bijective point-shift, the Palm probability is invariant under random translations induced by f. I will go through examples of bijective point-shifts. Time allowing, I will mention a few results from Baccelli & Haji-Mirsadeghi [2013], which extends this type of connection for non-bijective point-shifts. Submitted by
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