Upcrossing inequalities for stationary sequences

  • Mike Hochman | Hebrew University

Let g be a function which assigns to each stationary process Xn and to each sample X1, X2 ,…, Xn of the process a real number g(X1, … ,Xn), which may also depend on the distribution of the process. I’ll discuss how one can obtain effective bounds on the probability that the sequence g(X1, …, Xn) crosses a fixed interval some number of times in terms of a quantity measuring the “average sub-additivity” of g. Applications include universal upcrossing inequalities for Kingman’s sub-additive ergodic theorem, for the Shannon-McMillan-Breiman theorem, and for the Kolmogorov complexity statistic.

Speaker Details

I was born in 1976 in Jerusalem, Israel, where I also spent most of my childhood. As a teenager I was mainly interested in reading science fiction and playing soccer and chess. After graduating from high school in 1994 I spent the next three years in the Israeli Army, serving in the signals corps. During this period I took some correspondence courses in mathematics at the Open University. Following my discharge I travelled a abroad a little and did some odd jobs, and finally enrolled in the Hebrew University’s math and computer science program, graduating in 2001. By this time I was hooked; I completed my M.A. in mathematics in 2003 and am completing my Ph.D. this year. In between I still play soccer, though chess has fallen into disfavor, and when I want science fiction I just read the newspaper.

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