The classical conditional expectation with respect to [sigma]-algebras, on probability measure spaces, has been extended for infinite measure spaces. In this paper we consider conditional expectations with respect to [delta]-rings, on arbitrary measure spaces. An additional condition has to be...

Quantum mechanical analogues of Wiener processes are defined and their existence proved, in terms of which the field operators of extremal universally invariant representations of the canonical commutation relations are expressible as stochastic integrals. A noncommutative analogue of the Wiener...

Convergence of weighted sums of tight random elements {Vn} (in a separable Banach space) which have zero expected values and uniformly bounded rth moments (r 1) is obtained. In particular, if {ank} is a Toeplitz sequence of real numbers, then [Sigma]k=1[infinity] ankf(Vk) -- 0 in probability...

The "iterative instrumental variables" (IIV) method for estimating interdependent systems, originally referred to as a symmetric counterpart to the "fix-point" (FP) method, shares its symmetry properties with Durbin's iterative method for performing the "full information maximum likelihood"...

A common problem in multivariate analysis is that of minimising or maximising a function f of a positive semidefinite matrix A subject possibly to AX = 0. Typically A is a variance-covariance matrix. Using the theory of nearest point projections in Hilbert spaces, it is shown that the solution...

The variance of a quadratic function of the random variables in a linear model is minimized to obtain locally best unbiased estimators (MIVQUE) of variance components. Condition for such estimators to be independent of the kurtosis of the variables is given. When the variables are normally...

Asymptotic expansions are given for the distributions of latent roots of matrices in three multivariate situations. The distribution of the roots of the matrix S1(S1 + S2)-1, where S1 is Wm(n1, [Sigma], [Omega]) and S2 is Wm(n2, [Sigma]), is studied in detail and asymptotic series for the...

The present paper is devoted to the study of the direct limits of direct systems of measure (resp. probability) spaces. If I is a right directed preordered set, (E[alpha])[alpha][set membership, variant]I a family of sets indexed by I, G = [up curve][alpha][set membership, variant]I E[alpha] -...

A sequence (Xn) of random variables adapted to an ascending (asc.) sequence n of [sigma]-algebras is an amart iff EX[tau] converges as [tau] runs over the set T of bounded stopping times. An analogous definition is given for a descending (desc.) sequence n. A systematic treatment of amarts is...