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On the Relation of One-Dimensional Diffusions on Natural Scale and Their Speed Measures

Author

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  • David Criens

    (Albert-Ludwigs University of Freiburg)

Abstract

It is well known that the law of a one-dimensional diffusion on natural scale is fully characterized by its speed measure. Stone proved a continuous dependence of such 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.

Suggested Citation

  • David Criens, 2023. "On the Relation of One-Dimensional Diffusions on Natural Scale and Their Speed Measures," Journal of Theoretical Probability, Springer, vol. 36(4), pages 2339-2358, December.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:4:d:10.1007_s10959-023-01247-8
    DOI: 10.1007/s10959-023-01247-8
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