Mathematical Sciences: Large Deviations and the Law of the Iterated Logarithm in Banach Spaces

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The investigator plans to study two problems. The first problem of large deviations has deep theoretical consequences as well as applications in statistical physics and mathematical statistics. The investigator hopes eventually to prove a general result on lower bounds for large deviations in case of vector- valued functionals of Markov chains. He has already established several links necessary to prove this result. The second problem hopes to settle the major open question in the field of the law of iterated logarithms in Banach spaces viz., the identification of the limits and the underlying problem of obtaining sharp exponential bounds for sums of independent random vectors.