Volume 11, Issue 1

We consider stochastic processes from the Orlicz space of random variables. Conditions of boundedness as well as estimates of the distribution of the supremum of these processes are obtained. Stochastic processes from the Orlicz spaces generated by Orlicz N -functions from spaces Δ 2 and Δ 2 are investigated in more details.

We are interested in the distribution of distance between two random points in a cube. It is well known, that the derivation of the formulae of the distribution function of interest implies integration problems which are almost intractable. We show, that the problem may be successfully solved using a symbolic computation tool.

We study distribution laws of diffusion type processes and corresponding generalized functions. The stochastic integral equation satisfed by these generalized functions is derived.

We consider certain random matrices with pairwise uncorrelated, but dependent entries, that do not belong to the Marchenko-Pastur ensemble (sample covariance matrices), and obtain bounds on their largest eigenvalue. The results show that the higher order correlations have a strong influence on the norm. While the proofs follow the well-known method of calculating the expectation of the trace of high powers of the matrices, the ensuing combinatorial problems are of a novel type.