Tail probabilities and almost sure bounds for martingales
This thesis contains a study of martingales. Some well-known results of probability theory are extended to the martingale context. Many of the extensions are best-possible in a sense to be made precise in the relevant part of the text. One result provides a characteristic difference between martingales and sums of independent random variables. Extensions to martingales of certain limit theorems for maxima of suras of independent random variables are given; these results are in a form...[Show more]
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