Mathematical Sciences: Laws of the Iterated Logarithm and Strong Approximations

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The principal investigator is working on problems in probability theory concerning the law of the iterated logarithms (LIL) and strong approximations. In particular, the investigator will work on convergence rates in the LIL in Hilbert spaces, infinite dimensional versions of the Darling-Erdos theorem and Chung type LIL's, and strong approximations for sums of independent Banach space value random variables. Properties of sums of independent random variables have been of interest to probabilists and statisticians for a long time. The law of the iterated logarithm gives a very precise bound on how fast a sum of random variables grows.