Almost sure invariance principles for partial sums of weakly dependent random variables - Philipp, Walter, 1936-; Stout, William F., 1940- (Memoirs of the American Mathematical Society, 1975)
A strong revival of interest in the law of the iterated logarithm and related asymptotic fluctuation results has occurred in the last decade, stimulated by two remarkable papers by Volker Strassen. In these papers, Strassen introduces a new method for establishing such fluctuation results for sums of independent random variables and for martingales. Strassen's almost sure invariance principle for martingales states that each martingale satisfying a certain second moment condition is with probability on "close" to a Brownian motion. In this monograph we investigate the asymptotic fluctuation behavior of sums of weakly dependent random variables, such as lacunary trigonometric mixing, and Gaussian sequences.