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...

We establish a connection between the function space BMO and theory of quasisymmetric mappings on \emph{spaces homogeneous type} $\widetilde{X} :=(X,\rho,\mu)$. The is that logarithm generalised Jacobian an $\eta$-quasisymmetric mapping $f: \widetilde{X} \rightarrow \widetilde{X}$ always in $\rm{BMO}(\widetilde{X})$. In course proving this result, we first show $\widetilde{X}$, reverse-H\"{o}ld...

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...

It is well-known that there is an intimate connection between the RadonNikodym property and martingale convergence in a Banach space. This connection can be "localized" to a closed bounded convex subset of a Banach space. In this paper we are interested primarily in this connection for a bounded convex set which is not closed. If C is a bounded convex set in a locally convex space, C is said to...

Let (X,%, ß) be a u-finite measure space and 3£ be a linear subspace of S?x{ft) with supp^ = X. The following inverse problem is treated: Which sets A £ 21 are "^-determined" within the class of all functions g e S? ...