Related papers: Probability measure annihilating all finite-dimens…
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a…
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course…
Building on recent results regarding symmetric probabilistic constructions of countable structures, we provide a method for constructing probability measures, concentrated on certain classes of countably infinite structures, that are…
We construct surface measures associated to Gaussian measures in separable Banach spaces, and we prove several properties including an integration by parts formula.
In this paper we collect several examples of convergence of functions of random processes to generalized functionals of those processes. We remark that the limit is always finitely absolutely continuous with respect to Wiener measure. We…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in $\bf R$.…
We develop a family of infinite-dimensional Banach manifolds of measures on an abstract measurable space, employing charts that are "balanced" between the density and log-density functions. The manifolds, $(\tilde{M}_{\lambda},\lambda\in…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
A pivotal problem in Bayesian nonparametrics is the construction of prior distributions on the space M(V) of probability measures on a given domain V. In principle, such distributions on the infinite-dimensional space M(V) can be…
We derive the isoperimetric profile of Gaussian type for an absolutely continuous probability measure on Euclidean spaces with respect to the Lebesgue measure, whose density is a radial function.The key is a generalization of the Poincar\'e…
We show the existence of the local dimension of an invariant probability measure on an infinitely generated self-affine set, for almost all translations. This implies that an ergodic probability measure is exactly dimensional. Furthermore…
Quasi-invariant and pseudo-differentiable measures on a Banach space $X$ over a non-Archimedean locally compact infinite field with a non-trivial valuation are defined and constructed. Measures are considered with values in non-Archimedean…
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…
In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive Banach space is always primary.…
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…
Let $\gamma$ be a Gaussian measure on a locally convex space and $H$ be the corresponding Cameron-Martin space. It has been recently shown by L. Ambrosio and A. Figalli that the linear first-order PDE $$ \dot{\rho} + \mbox{div}_{\gamma}…
The framework of this paper is that of risk measuring under uncertainty, which is when no reference probability measure is given. To every regular convex risk measure on ${\cal C}_b(\Omega)$, we associate a unique equivalence class of…
We develop a family of infinite-dimensional (non-parametric) manifolds of probability measures. The latter are defined on underlying Banach spaces, and have densities of class $C_b^k$ with respect to appropriate reference measures. The case…
This short review is devoted to measures on infinite dimensional spaces. We start by discussing product measures and projective techniques. Special attention is paid to measures on linear spaces, and in particular to Gaussian measures.…
We consider the Banach space consisting of real-valued continuous functions on an arbitrary compact metric space. It is known that for a prevalent (in the sense of Hunt, Sauer and Yorke) set of functions the Hausdorff dimension of the image…