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SUMMARY:Prakash Panangaden (McGill)
DTSTART:20200408T170000Z
DTEND:20200408T180000Z
DTSTAMP:20260423T024534Z
UID:ACTUCR/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ACTUCR/8/">A
  categorical view of conditional expectation</a>\nby Prakash Panangaden (M
 cGill) as part of ACT@UCR\n\n\nAbstract\nThis talk is a fragment from a la
 rger work on approximating Markov processes. I will focus on a functorial 
 definition of conditional expectation without talking about how it was use
 d. We define categories of cones---which are abstract versions of the fami
 liar cones in vector spaces---of measures and related categories cones of 
 Lₚ functions. We will state a number of dualities and isomorphisms betwe
 en these categories. Then we will define conditional expectation by exploi
 ting these dualities: it will turn out that we can define conditional expe
 ctation with respect to certain morphisms. These generalize the standard n
 otion of conditioning with respect to a sub-sigma algebra. Why did I use t
 he plural? Because it turns out that there are two kinds of conditional ex
 pectation\, one of which looks like a left adjoint (in the matrix sense no
 t the categorical sense) and the other looks like a right adjoint. I will 
 review concepts like image measure\, Radon-Nikodym derivatives and the tra
 ditional definition of conditional expectation. This is joint work with Ph
 ilippe Chaput\, Vincent Danos and Gordon Plotkin. \n
LOCATION:https://researchseminars.org/talk/ACTUCR/8/
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