Probability seminar: Variance of partial sums of stationary processes

20 March 2015, 3.40 PM - 20 March 2015, 4.40 PM

George Deligiannidis, University of Oxford

SM3, School of Mathematics

George Deligiannidis, University of Oxford

Variance of partial sums of stationary processes

We give necessary and sufficient conditions for the variance of the partial sums of stationary processes to be regularly varying in terms of the spectral measure associated with the shift operator. In the case of reversible Markov chains, or with normal transition operator we also give necessary and sufficient conditions in terms of the spectral measure of the transition operator. The two spectral measures are then linked through the use of harmonic measure.

This is joint work with S. Utev (University of Leicester, UK) and M. Peligrad (University of Cincinnati, USA).

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Organisers: Marton Balazs, Haeran Cho

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