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

本研究将研究与样本重复使用过程有关的概率问题，称为自举。研究者已经在这个领域证明了一些结果。现在他建议将结果扩展到方差无穷大的情况。当使用经验累积分布函数的平滑和修剪版本进行重采样时，它还将研究均值的自举分布的行为。第二部分研究了关键的简单分支过程。当分支过程中的方差为无穷大时，研究者将发现最大值的均值在n代之前的极限行为。这位研究人员是“几乎再生过程”概念的创始者，他将继续他的研究。

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.