Let (Xn)n[epsilon] be a sequence of real, independent, not necessarily identically distributed random variables (r.v.) with distribution functions FXn, and Sn = [Sigma]i=1n Xi. The authors present limit theorems together with convergence rates for the normalized sums [phi](n)Sn, where [phi]: --...

Nonlinear filtering process [pi]t, t = 0 of a Markovian signal process with the state space S is regarded as a stochastic process with values in the set of all probability distributions over S. Under a suitable condition, it is shown that the filtering process is Markovian and that the invariant...

The general form of characteristic functionals of Gaussian measures in spaces of type 2 and cotype 2 is found. Under the condition of existence of an unconditional basis this problem is solved for spaces not containing l[infinity]n uniformly. The solution uses the language of absolutely summing...

For forward and reverse martingale processes, weak convergence to appropriate stochastic (but, not necessarily, Wiener) processes is studied. In particular, it is shown that martingale processes are tight under a uniformly integrability condition, and also, convergence of finite dimensional...

Consider the stochastic processes X1, X2,... and [Lambda]1, [Lambda]2,... where the X process can be thought of as observations on the [Lambda] process. We investigate the asymptotic behavior of the conditional distributions of Xt+v given X1,..., Xt and [Lambda]t+v given X1,..., Xt with regard...

Let V1,..., Vm, W1,..., Wn be independent p - 1 random vectors having multivariate normal distributions with common nonsingular covariance matrix [Sigma] and with EW[alpha] = 0, [alpha] = 1,..., n. In this canonical form of the multivariate linear model, the problem is to test H: EV[alpha] az...

Quantum statistical decision theory arises in connection with applied problems of optimal detection and processing of quantum signals. In this paper we give a systematic treatment of this theory, based on operator-valued measures. We study the existence problem for optimal measurements and give...

Let ([Omega], , [mu]) be a finite measure space and a real separable Banach space. Measurability and integrability are defined for multivalued functions on [Omega] with values in the family of nonempty closed subsets of . To present a theory of integrals, conditional expectations, and...

The concepts of absolute continuity and singularity for operator-valued measures are introduced and Radon-Nikodym and Lebesgue decomposition theorems for such measures are established. These theorems reduce directly to the classical results in the scalar case. The results have interesting...

A decomposition termed the matrix-decomposition of the MANOVA hypothesis is discussed. On the basis of this decomposition the Hotelling-Lawley trace statistic is derived as a Union-Intersection (U-I) statistic. A new derivation of the c1-statistic is obtained as a particular case of the U-I...