Mathematical Sciences: Laws of the Iterated Logarithm and Strong Approximations

首席研究员正在研究 关于迭代律的概率论 (LIL)强逼近。 特别是 研究人员将在希尔伯特的LIL中研究收敛速度 空间，无限维版本的达令-鄂尔多斯 定理和Chung型LIL的，以及和的强逼近 独立的Banach空间值随机变量。 独立随机变量和的性质具有 很长一段时间以来， 时间 重对数定律给出了一个非常精确的 取决于随机变量之和的增长速度

The principal investigator is working on problems in probability theory concerning the law of the iterated logarithms (LIL) and strong approximations. In particular, the investigator will work on convergence rates in the LIL in Hilbert spaces, infinite dimensional versions of the Darling-Erdos theorem and Chung type LIL's, and strong approximations for sums of independent Banach space value random variables. Properties of sums of independent random variables have been of interest to probabilists and statisticians for a long time. The law of the iterated logarithm gives a very precise bound on how fast a sum of random variables grows.