Gaussian measures on some non-Banach spaces of measurable functions are investigated. The main result is that every Gaussian measure on a separable Orlicz space L[phi] is an extension of the canonical cylindrical Gaussian distribution on the RKHS. As an application we obtain some results...

The aim of this paper is to give a functional form for the central limit theorem obtained by Bradley for strong mxing sequences of random variables, under a certain assumption about the size of the maximal coefficients of correlations. The convergence of the moments of order 2 + [delta] in the...

The usual assumption in the classical errors-in-variables problem of independent measurement errors cannot necessarily be maintained when the data are time series; errors may be strongly serially correlated, possibly containing seasonal effects and trends. When it is possible to identify...

This work is devoted to the study of the behavior of stochastic evolution equations, obtained from stochastic flows, under the multiplicative transformations corresponding to the flows of Cameron-Martin transformations.

A useful theorem to determine the group of all affine transformations leaving a multivariate normal test problem invariant is presented. For the MANOVA and GMANOVA test problems the well-known invariance groups are shown to be the greatest invariance-groups.

Consider a simple branching diffusion process, which is a branching process in which the individuals move and live and die in space. The offspring distribution has finite moments of all orders. A parametric estimation theory is presented, using time slice data. This involves the use of third...

Two parameter Stochastic processes {Xz([omega]), [omega] [set membership, variant] [Omega], z [set membership, variant] +2} which are L2 integrators are characterized through associated bimeasures defined on the product spaces ([Omega] - +2) - ([Omega] - +2) and and [Omega] - +2 - +2. It is also...

The central limit (or fluctuation) phenomena are discussed in the interacting diffusion system. The tightness in the Kolmogorov-Prokhorov sense is proved for a sequence of distribution valued processes arising from finite particle systems. Further, the stochastic differential equation for the...

The distribution theory is developed for a generalized least squares estimator of the growth curve model. A special case of the estimator is the maximum likelihood estimator which is weighted by the sample covariance matrix. The distribution of two conditional forms of the estimator are derived...