A general LIL for B-valued geometrically weighted series under dependent assumption.

Let { X, X; n≧0} be a sequence of identically distributed ψ-mixing dependent random variables taking values in a type 2 Banach space B with topological dual B. Considering the geometrically weighted series $\xi(\beta)= \sum_{n=0}^{\infty}\beta^{n}X_{n}$ for 0< β<1, a general law of the iterated logarithm for ξ( β) is obtained without second moment. [ABSTRACT FROM AUTHOR]