We establish large deviation properties valid for almost every sample path of a class of stationary mixing processes (X1,...,Xn,...). These properties are inherited from those of and describe how the local fluctuations of almost every realization of Sn deviate from the almost sure behavior....

A new class of random multiplicative and statistically self-similar measures is defned on IR. It is the limit of measure-valued martingales constructed by multiplying random functions attached to the points of a statistically self-similar Poisson point process in a strip of the plane. Several...