On the regular representation of measures

Abstract

We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class $C^k$. The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular representability.

19 pages

References in corpus (1)

• Representation of Markov chains by random maps: existence and regularity conditions

Cited by in corpus (1)

• Probabilistic morphisms and Bayesian nonparametrics