Strong Limit Theorems for Mixing Random Variables with Values in Hilbert Space and their Applications
Olimjon Sh. SharipovDepartment of Probability Theory, Institute of Mathematics, Uzbek Academy of Sciences, 29, F. Khodjaev str., 700143, Tashkent, Uzbekistan
ABI
Abstract
We consider strong limit theorems such as bounded and compact laws of the iterated logarithm and an almost sure invariance principle for mixing random variables with values in Hilbert space. Applying these results we prove an almost sure invariance principle for U-statistics as well.