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2014 From minimal embeddings to minimal diffusions
Alexander Cox, Martin Klimmek
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Electron. Commun. Probab. 19: 1-13 (2014). DOI: 10.1214/ECP.v19-2889

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.

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Alexander Cox. Martin Klimmek. "From minimal embeddings to minimal diffusions." Electron. Commun. Probab. 19 1 - 13, 2014. https://doi.org/10.1214/ECP.v19-2889

Information

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

zbMATH: 1312.60093
MathSciNet: MR3225865
Digital Object Identifier: 10.1214/ECP.v19-2889

Subjects:
Primary: 60J60
Secondary: 60G40 , 60J55

Keywords: diffusion , local-martingales , minimality , Skorokhod embedding problem

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