Recently, Rosinski and Woyczynski have given necessary and sufficient conditions for the existence of the double integral with respect to a symmetric stable process of index [alpha] in [1, 2). In their approach the double integral is defined as an iterated Itô-type integral. We show here that...

In this paper, we study almost sure central limit theorems for sequences of functionals of general Gaussian fields. We apply our result to non-linear functions of stationary Gaussian sequences. We obtain almost sure central limit theorems for these non-linear functions when they converge in law...

The multifractional Brownian motion (MBM) processes are locally self-similar Gaussian processes. They extend the classical fractional Brownian motion processes by allowing their self-similarity parameter H[set membership, variant](0,1) to depend on time. Two types of MBM processes were...

Let (X1, X2) be a symmetric [alpha]-stable random vector with 0 [alpha] 2. Its distribution is characterized by a finite measure [GH] on the unit circle called the spectral measure. It is known that if [GH] satisfies some integrability condition then the conditional moment E[X2pX1 = x] can...

Consider a vector of multilinear polynomial-form processes with either short or long memory components. The components have possibly different coefficients but same noise elements. We study the limit of the normalized partial sums of the vector and identify the independent components.