Speaker:

Michael Woodroofe

Title:

Law of the Iterated Logarithm For Stationary Processes

Abstract:

The Law of Large Numbers, the Central Limit Theorem, and the Law of the Iterated Logarithm for independent and identically distributed sequences of random variables are three central, perhaps dominant, results of classical probability theory. The Ergodic Theorem provides an extension of the Law of Large Numbers to sequences that are dependent, but stationary. The Central Limit Theorem and Law of the Iterated Logarithm do not extend as completely, but only under additional conditions that effectively limit the amount of dependence. During the past decade there has been some progress on understanding the Central Limit Theorem for stationary processes, resulting in conditions that are sufficient and nearly necessary, at least for the conditional version of the Central Limit Theorem. The talk will present recent efforts to modify the arguments leading to the Central Limit Theorem to obtain a Law of the Iterated Logarithm. It will begin with a selective review of work on the Central Limit Theorem and then explore the modifications. This is joint work with Ou Zhao.

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