On the relation of one-dimensional diffusions on natural scale and their speed measures
Probability
2021-12-02 v1
Abstract
It is well-known that the law of a one-dimensional diffusion on natural scale is fully characterized by its speed measure. C. Stone proved a continuous dependence of diffusions on their speed measures. In this paper we establish the converse direction, i.e. we prove a continuous dependence of the speed measures on their diffusions. Furthermore, we take a topological point of view on the relation. More precisely, for suitable topologies, we establish a homeomorphic relation between the set of regular diffusions on natural scale without absorbing boundaries and the set of locally finite speed measures.
Keywords
Cite
@article{arxiv.2112.00072,
title = {On the relation of one-dimensional diffusions on natural scale and their speed measures},
author = {David Criens},
journal= {arXiv preprint arXiv:2112.00072},
year = {2021}
}