The finitely additive nonlinear filtering problem for the model yt = ht(Xt)+et is solved when the function h is unbounded and satisfies no growth conditions whatever.

A concept of divisibility is introduced for stochastic difference equations. Infinite divisibility then leads to a continuous time process in which a nested sequence of divisible stochastic difference equations can be embedded.

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...

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...

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...

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.