Mathematical Sciences: Some Problems on Laws of the IteratedLogarithm and Strong Approximations

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One of the basic results of probability is the so-called law of the iterated logarithm (LIL), which provides a precise description of the asymptotic behavior of sums of independent random variables. For many applications one needs a more general framework than in the classical case which deals with real-valued random variables. The main purpose of this research is to study LIL results and some related problems such as strong approximation and certain weak convergence results in general Banach spaces. This research will extend results in the theory of probability. In many applications a more general framework is needed, and this research will help provide it.