Let X = {X(t), t ≥ 0} be a Brownian motion or a spectrally negative stable process of index 1 < α < 2. Let E = {E(t), t ≥ 0} be the hitting time of a stable subordinator of index 0 < β < 1 independent of X . We use a connection between X(E(t)) and the stable subordinator of index β/α to derive information on the path behavior of X(Et). This is an extension of the connection of iterated Brownian...

We prove a general functional limit theorem for mul-tiparameter fractional Brownian motion. The functional law of the iterated logarithm, functional Lévy's modulus of continuity and many other results are its particular cases. Applications to approximation theory are discussed.

In this paper we establish some limsup results and a generalized uniform law of the iterated logarithm (LIL) for the increments of partial sums of a strictly stationary and linearly positive quadrant dependent (LPQD) sequence of random variables.