Laws of the iterated logarithm for the empirical characteristic function (Q1119254)

Let X be a real-valued random variable with characteristic function c(t). Let \(c_ n(t)\) be the n-th empirical characteristic function associated with X. Strong limits of \[ C_ n(t)=\sqrt{n}(c_ n(t)-c(t)),\quad t\in [-1,1], \] in the Banach space of continuous, complex-valued functions on [-1,1] are investigated. Necessary and sufficient conditions in terms of c(t) are obtained for \(C_ n(t)\) to satisfy bounded and compact laws of the iterated logarithm.