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...

1 Summary The Radon-Nikodym derivative between a centered fractional Brownian motion Z and the same process with constant drift is derived by nding an integral transformation which changes Z to a process with independent increments. A representation of Z through a standard Brownian motion on a nite interval is given. The maximum likelihood estimator of the drift and some other applications are ...

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.

Let X and Y be Polish spaces with non-atomic Borel measures μ and ν of full support. Suppose that T and S are ergodic non-singular homeomorphisms of (X, μ) and (Y, ν) with continuous Radon-Nikodym derivatives. Suppose that either they are both of type III1 or that they are both of type IIIλ, 0 < λ < 1 and, in the IIIλ case, suppose in addition that both ‘topological asymptotic ranges’ (defined ...

We present a short survey of some very recent results on the finitely additive white noise theory. We discuss the Markov property of the solution of a stochastic differential equation driven directly by a white noise, study the Radon-Nikodym derivative of the measure induced by nonlinear transformation on a Hilbert space with respect to the canonical Gauss measure thereon and obtain a represent...

Abstract For a pair of bounded linear Hilbert space operators A and B one considers the Lebesgue type decompositions with respect to into an almost dominated part singular part, analogous decomposition for measures in which case speaks absolutely continuous part. complete parametrization all will be given, uniqueness such characterized. In addition, it shown that has abstract Radon–Nikodym deri...

These notes give various references to the literature that I will not, for reasons of brevity, give during the lectures themselves. 1. Gaussian Measures A comprehensive reference for Gaussian measures is [Bog98]. This book works in the generality of locally convex topological spaces, and has material on Gaussian measure on Banach and Hilbert spaces as particular cases. A similar book, focussed ...

is to be minimized over control processes Y whose increments take values in a cone Y of Rp , keeping the state process X = x+B+GY in a cone X of Rk , k ≤ p. Here, x ∈ X, B is a Brownian motion with drift b and covariance , G is a fixed matrix, and Y ◦ is the Radon–Nikodym derivative dY/d|Y |. Let L=−(1/2)trace( D2)− b ·D where D denotes the gradient. Solutions to the corresponding dynamic progr...

We present linear-time estimators for three popular covariate shift correction and propensity scoring algorithms: logistic regression(LR), kernel mean matching(KMM) [19], and maximum entropy mean matching(MEMM)[20]. This allows applications in situations where both treatment and control groups are large. We also show that the last two algorithms differ only in their choice of regularizer (l2 of...