Functional central limit theorem and Strassen's law of the iterated logarithms for weakly multiplicative systems
A sequence of r.v.'s \(X_ 1,X_ 2,..\). is called a multiplicative system if E \(X_{i_ 1}X_{i_ 2}...X_{i_ k}=0\) \((i_ 1<i_ 2<...<i_ k\); \(k=1,2,...)\). The central limit theorem and the law of iterated logarithm for multiplicative systems were proved (under some further restrictions) by several authors. In the present paper the weak and strong invariance principles are proved for multiplicative systems. The conditions used by the author meet with the weakest conditions used earlier to prove the central limit theorem and the law of iterated logarithm.
scientific article; zbMATH DE number 4194841