For a general stochastic signal in white noise absolute continuity is proved and the Radon-Nikodym derivative is given. These results were stated in a previous paper (Duncan 1968). Independent of the absolute continuity result, a modification is proved for the hypothesis with signal present.

In this article we define measurable multifunctions in nonseparable Banach spaces, prove a weak compactness criterion for the selectors of multifunctions integrably bounded, characterize Banach spaces that have the Radon–Nikodym property by means of convergence of multivalued martingales, generalize some recent results on convergence of set-valued conditional expectations, and give some applica...

We construct a class of iterated stochastic integrals with respect to Brownian motion on an abstract Wiener space which allows for the definition motions general infinite-dimensional nilpotent Lie groups based spaces. then prove that Cameron–Martin type quasi-invariance result holds associated heat kernel measures in non-degenerate case, and give estimates Radon–Nikodym derivative. also log Sob...

In the signal-processing literature, a frame is mechanism for performing analysis and reconstruction in Hilbert space. By contrast, quantum theory, positive operator-valued measure (POVM) decomposes Hilbert-space vector purpose of computing measurement probabilities. Frames their most common generalizations can be seen to give rise POVMs, but does every reasonable POVM arise from type frame? We...

Abstract It is proved that each Gaussian cocycle over a mildly mixing transformation either coboundary or sharply weak mixing. The class of non-singular infinite direct products T transformations $T_n$ , $n\in \mathbb N$ finite type studied. shown if mixing, the sequence Radon–Nikodym derivatives asymptotically translation quasi-invariant and conservative then Maharam extension This technique p...