We establish an invariance principle for a general class of stationary random fields indexed by Zd, under Hannan … principle by developing an orthomartingale approximation. Our invariance principle improves known results in the literature, and … second we establish a coboundary decomposition for certain stationary random fields. At last, we obtain an invariance …

, the weak invariance principle takes place. The question whether for strictly stationary sequences with finite second … moments and a weaker type (α, β, ρ) of mixing the central limit theorem implies the weak invariance principle remained open. …

. When the largest noise has the same order as the maximal displacement of the random walk, we establish an invariance … principle for the maximum process in the Skorohod topology. The limiting process is the maximum process of the fractional …

are shown. Firstly, a bootstrap Invariance Principle is derived pointwise in i, obtaining an upper bound for the order of …

general form of the quenched Invariance Principle for walks in doubly stochastic environments with zero local drift …