On Gaussian measures equivalent to Wiener measure

Absolute Continuity between the Wiener and Stationary Gaussian Measures

It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spe...

The Entropy Distance between the Wiener and Stationary Gaussian Measures

Investigating the entropy distance between the Wiener measure,Wt0,τ , and stationary Gaussian measures, Qt0,τ on the space of continuous functions C[t0 − τ, t0 + τ ], we show that in some cases this distance can essentially be computed. This is done by explicitly computing a related quantity which in effect is a valid approximation of the entropy distance, provided it is sufficiently small; thi...

On Gaussian Processes Equivalent in Law to Fractional Brownian Motion

We consider Gaussian processes that are equivalent in law to the fractional Brownian motion and their canonical representations. We prove a Hitsuda type representation theorem for the fractional Brownian motion with Hurst index H [ 2 . For the case H> 2 we show that such a representation cannot hold. We also consider briefly the connection between Hitsuda and Girsanov representations. Using the...

Wiener measure and Donsker’s theorem

R-bounded Fuzzy Measures Are Equivalent to Ε-possibility Measures

Traditional probabilistic description of uncertainty is based on additive probability measures. To describe nonprobabilistic uncertainty, it is therefore reasonable to consider non-additive measures. An important class of non-additive measures are possibility measures, for which μ(A ∪ B) = max(μ(A), μ(B)). In this paper, we show that possibility measures are, in some sense, universal approximat...