It is shown that for a wide class of signal processes and bounded g, the conditional expectation [pi](g, y) in the white noise filtering model is a C[infinity]-functional of the observations in the sense that [pi](g, y) and its Fréchet derivatives (which exist) are random variables on the...

In this paper we formulate and prove a general principle which enables us to deduce limit theorems for a sequence of random variables on a finitely additive probability space.

We show that a field X(m,n) is strongly periodically correlated with period (M,N) if and only if there exist commuting unitary operators, U1 and U2 that shift the field unitarily by M and N along the respective coordinates. This is equivalent to a field whose shifts on a subgroup are unitary. We...

An explicit formula is obtained for the nonlinear predictor of Y(t) = X(t)2 - E(X(t)2), where X(t) is an N-ple Gaussian Markov process.

Suppose on a probability space ([Omega], F, P), a partially observable random process (xt, yt), t = 0; is given where only the second component (yt) is observed. Furthermore assume that (xt, yt) satisfy the following system of stochastic differential equations driven by independent Wiener...

For weakly stationary stochastic processes taking values in a Hilbert space, spectral representation and Cramér decomposition are studied. Using these ideas and the moving average representation for such processes established earlier by the authors, some necessary and sufficient spectral...

Nonanticipative linear transformations of the two-parameter Wiener process W are studied. It is shown that they induce measures equivalent to two-parameter Wiener measure and the corresponding Radon-Nikodym derivatives are calculated. A two-parameter extension of Girsanov's theorem is...

The paper develops the spectral theory corresponding to the various time domain Wold decompositions of a discrete two-parameter stationary second-order random field (ssorf). Appropriate Szegö-type error formulas are established. Minimality and interpolability are defined for ssorf's and...