Electronic Communications in Probability

From minimal embeddings to minimal diffusions

Alexander Cox and Martin Klimmek

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Abstract

We show that there is a one-to-one correspondence between diffusions and the solutions of the Skorokhod Embedding Problem due to Bertoin and Le-Jan. In particular, the minimal embedding corresponds to a "minimal local martingale diffusion", which is a notion we introduce in this article. Minimality is closely related to the martingale property. A diffusion is minimal if it minimises the expected local time at every point among all diffusions with a given distribution at an exponential time. Our approach makes explicit the connection between the boundary behaviour, the martingale property and the local time characteristics of time-homogeneous diffusions.

Article information

Source
Electron. Commun. Probab. Volume 19 (2014), paper no. 34, 13 pp.

Dates
Accepted: 11 June 2014
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465316736

Digital Object Identifier
doi:10.1214/ECP.v19-2889

Mathematical Reviews number (MathSciNet)
MR3225865

Zentralblatt MATH identifier
1312.60093

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60] 60J55: Local time and additive functionals

Keywords
diffusion minimality local-martingales Skorokhod embedding problem

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Cox, Alexander; Klimmek, Martin. From minimal embeddings to minimal diffusions. Electron. Commun. Probab. 19 (2014), paper no. 34, 13 pp. doi:10.1214/ECP.v19-2889. https://projecteuclid.org/euclid.ecp/1465316736


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