CROSS-MOMENTS COMPUTATION FOR STOCHASTIC CONTEXT-FREE GRAMMARS

In this paper we consider the problem of efficient computation of cross-moments of a vector random variable represented by a stochastic context-free grammar. Two types of cross-moments are discussed. The sample space for the first one is the set of all derivations of the context-free grammar, and the sample space for the second one is the set of all derivations which generate a string belonging to the language of the grammar. In the past, this problem was widely studied, but mainly for the cross-moments of scalar variables and up to the second order. This paper presents new algorithms for computing the cross-moments of an arbitrary order, while the previously developed ones are derived as special cases.

CROSS-MOMENTS COMPUTATION FOR STOCHASTIC CONTEXT-FREE GRAMMARS

In this paper we consider the problem of efficient computation of cross-moments of a vector random variable represented by a stochastic context-free grammar. Two types of cross-moments are discussed. The sample space for the first one is the set of all derivations of the context-free grammar, and the sample space for the second one is the set of all derivations which generate a string belonging to the language of the grammar. In the past, this problem was widely studied, but mainly for the cross-moments of scalar variables and up to the second order. This paper presents new algorithms for computing the cross-moments of an arbitrary order, while the previously developed ones are derived as special cases.

On a random solution of a nonlinear perturbed stochastic integral equation of the Volterra type

The object of this present paper is to study a nonlinear perturbed stochastic integral equation of the formwhere ω ∈ Ω, the supporting set of the complete probability measure space (Ω A, μ). We are concerned with the existence and uniqueness of a random solution to the above equation. A random solution, x(t; ω), of the above equation is defined to be a vector random variable which satisfies the equation μ almost everywhere.

The characteristic functions of functions

The characteristic functions of various functions of a real or vector random variable are expressed in terms of the characteristic function of that variable. In the examples there is special emphasis on the stable distributions that have real characteristic functions. Some of the results suggest the practicability of generalizing traditional multivariate analysis beyond the multi-Gaussian model.