On the central limit theorem and law of the iterated logarithm for stationary processes with applications to linear processes

Many of the proofs of various central limit theorems and laws of the iterated logarithm for strictly stationary processes are based on approximating martingales. Here we study on this line the functional central limit theorem and law of the iterated logarithm for stationary processes, not necessarily possessing a coboundary decomposition, with applications to stationary linear processes.