Mathematical Sciences: Bootstrap Asymptotics in Statistics and Stochastic Processes and Limit Therorems for Branching and Almost Regenerative Processes

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This research will study the probability questions related to the sample re-use procedure called the bootstraping. The investigator has already proved a number of results in this area. Now he proposes to extend the results to the cases when the variance is infinite. It will also investigate the behavior of the bootstrap distribution of the mean when a smoothed and trimmed version of the empirical cummulative distribution function is used for resampling. For the second part of the research, critical simple branching processes are studied. The investigator will find the limiting behavior of the mean of the maximum up to the n-th generation when the variance in the branching process is infinite. The investigator, who has been the originator of the idea of almost regenerative processes, will continue his study of the same.