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We consider the algorithm of calculation of all constants of principal member of asymptotic of sojourn probability of multi-dimensional diffusion processes in small domain. The principal member defines normalizing coefficients for special limit theorems.

Stochastic processes with generalized Linnik marginals and various types of dependence structure, allowing for both short and long range dependence, are discussed in this paper.

Several two-boundary problems are solved for a semi-Markov random walk with a linear drift. The Laplace transforms of the joint distribution of the number of upward and downward intersection of the interval by the process. We also find the Laplace transforms of the boundary functionals of the processes reflected at their boundaries. The results obtained are applied for a special case when the jumps of the process are exponentially distributed.

We investigate ∈-upper and lower class functions for the maximum likelihood estimator of the drift parameter for stochastic processes satisfying linear stochastic differential equations driven by fractional Brownian motion.

A multidimensional classification of singularly continuous (w.r.t. the Lebesgue measure) probability measures in R 2 is introduced and a theorem on canonical representation of such measures is proven. A class of random elements on the unit square which is defined by a system of partitions generated by the Q *-representation of real numbers is introduced and studied in details. Conditions for the discreteness, absolute continuity resp. singular continuity (w.r.t. Lebesgue measure) of the corresponding probability measures are found. Metric, topological and fractal properties of the spectra of the corresponding probability distributions are investigated. A class of transformations preserving the Hausdorff-Besicovitch dimension of any subset of the unit square (DP-transformations) is also studied.