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Data Assimilation Seminar


Title: Slutsky's theorem in infinite dimension
Speaker(s): Jan Mandel
Affiliation: UCD Department of Mathematical and Statistical Sciences
When: Monday,  February 28, 2011
Time: 12:00 AM  -  2:00 PM
Where: CU building, Room 656

Slutsky's theorem states that if random elements u_n converge weakly to random element u, and v_n converge weakly to constant v (i.e., not random), then u_n+v_n converge to u+v, and similarly for product and quotient. The usual proof assumes that the random elements have values in finite dimensional vector space. However, there are proofs available that work in a metric space. Based on Van der Vaart's book, Wikipedia discussion and article, and Dudley's paper. Portmanteau theorem from Billingsley's book.

Please see http://ccm.ucdenver.edu/wiki/Jan_Mandel/Blog for links to the material.



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