Related papers: Conditional Expectations in Banach spaces with RNP

Let $M$ be a compact 1-manifold. Given a continuous function $g:M\to \mathbb R_+$ we consider the following ordinary differential equation: $\|\dot{f}(t)\|=g(t)$, where $f:M\to \mathbb R^2$. We construct a probability measure on the space…

We establish a necessary and sufficient condition for the differentiability of the distance function generated by a nonempty closed set K in a real normed linear space X under a proximinality condition on K. We do not assume the uniform…

We give a collection of explicit sufficient conditions for the true martingale property of a wide class of exponentials of semimartingales. We express the conditions in terms of semimartingale characteristics. This turns out to be very…

Let (X, d) be a quasi-convex, complete and separable metric space with reference probability measure m. We prove that the set of of real valued Lipschitz function with non zero point-wise Lipschitz constant m-almost everywhere is residual,…

For every couple of Hausdorff functions $ \psi$ and $\varphi $ verifying some mild assumptions, there exists a compact subset $ K $ of the Baire space such that the $ \varphi$-Hausdorff measure and the $ \psi$-packing measure on $ K$ are…

We provides some useful estimates for solving martingale representation problem under G-expectations. We also study the corresponding conditions for the existence and uniqueness.

We introduce the categories of quasi-measurable spaces, which are slight generalizations of the category of quasi-Borel spaces, where we now allow for general sample spaces and less restrictive random variables, spaces and maps. We show…

If $X$ is an almost transitive Banach space with amenable isometry group (for example, if $X=L^p([0,1])$ with $1\leqslant p<\infty$) and $X$ admits a uniformly continuous map $X\overset\phi\longrightarrow E$ into a Banach space $E$…

For a given element $f\in L^1$ and a convex cone $C\subset L^\infty$, $C\cap L^\infty_+=\{0\}$ we give necessary and sufficient conditions for the existence of an element $g\ge f$ lying in the polar of $C$. This polar is taken in…

In this paper, we investigate the geometric properties of the variable mixed Lebesgue-sequence space $\ell^{q(\cdot)} (L^{p(\cdot)})$ as a Banach space. We show that, if $ 1<q_-,p_-,q_+,p_+<\infty $, then $\ell^{q(\cdot)} (L^{p(\cdot)})$ is…

We investigate a possible definition of expectation and conditional expectation for random variables with values in a local field such as the $p$-adic numbers. We define the expectation by analogy with the observation that for real-valued…

The Bayesian perspective on inverse problems has attracted much mathematical attention in recent years. Particular attention has been paid to Bayesian inverse problems (BIPs) in which the parameter to be inferred lies in an…

A necessary and sufficient condition on a sequence $\{\mathfrak{A}_n\}_{n\in \mathbb{N}}$ of $\sigma$-subalgebras that assures convergence almost every where of conditional expectations is given.

From a given nuclear triplet we construct a nuclear triplet of sequence spaces and introduce a correlated Gaussian measure via the Bochner-Minlos theorem. Considering special types of correlation operators on such sequence spaces, certain…

For expectation functions on metric spaces, we provide sufficient conditions for epi-convergence under varying probability measures and integrands, and examine applications in the area of sieve estimators, mollifier smoothing,…

We consider the decreasing and the increasing $r$-excessive functions $\varphi_r$ and $\psi_r$ that are associated with a one-dimensional conservative regular continuous strong Markov process $X$ with values in an interval with endpoints…

An integral for a scalar function with respect to a multimeasure $N$ taking its values in a locally convex space is introduced. The definition is independent of the selections of $N$ and is related to a functional version of the…

Under mild assumptions, we prove that any random multifunction can be represented as the set of minimizers of an infinitely many differentiable normal integrand, which preserves the convexity of the random multifunction. We provide several…

For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…

We describe all metric spaces that have sufficently many affine functions. As an application we obtain a metric characterization of linear-convex subsets of Banach spaces.