Volume 20, Issue 2

Abstract. We continue the investigations in this paper which were considered in its first part. In particular, the problem of optimal filtration of one components of solution of nonlinear evolutionary differential equation in a Hilbert space H perturbing by Gaussian random process under observation of the second components of the same equation is considered. Using the results of the first part of this paper, here the algorithm for the calculation of an optimal estimate in the filtration problem is obtained.

Abstract. In this note, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous generator (left-or right-continuous). By a comparison theorem established here for RBDSDEs, we provide a minimal or a maximal solution to RBDSDEs.

Abstract. In this paper, we study evolutions in multidimensional spaces. By reducing multidimensional cases to the one-dimensional case, the properties of random evolutions in some semi-Markov media are studied.

Abstract. The Circular Law under Lindeberg condition for the independent entries of random matrices having zero expectations and double stochastic matrix of variances of their array is proven.

Abstract. Under conditions which are weaker than those used many years ago, the limit theorems for the n.s.f. of a pencil of nonsymmetric random matrices under Lindeberg condition are proved.