Probability measure functors preserving infinite-dimensional spaces

Product Preserving Functors of Infinite Dimensional Manifolds

The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of C∞-algebras.

Kullback-Leibler Approximation for Probability Measures on Infinite Dimensional Spaces

In a variety of applications it is important to extract information from a probability measure μ on an infinite dimensional space. Examples include the Bayesian approach to inverse problems and (possibly conditioned) continuous time Markov processes. It may then be of interest to find a measure ν, from within a simple class of measures, which approximates μ. This problem is studied in the case ...

Math 7770: Analysis and Probability on Infinite-Dimensional Spaces

• Rn has a natural measure space structure; namely, Lebesgue measure m on the Borel σalgebra. The most important property of Lebesgue measure is that it is invariant under translation. This leads to nice interactions between differentiation and integration, such as integration by parts, and it gives nice functional-analytic properties to differentiation operators: for instance, the Laplacian ∆ ...

Transformations of measure on infinite-dimensional vector spaces∗

Infinite dimensional Teichmüller spaces