From minimal embeddings to minimal diffusions

A.M.G. Cox, M. Klimmek

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Abstract

There is a fundamental connection between the class of diffusions in natural scale, and a certain class of solutions to the Skorokhod Embedding Problem (SEP). We show that the important concept of minimality in the SEP leads to the new and useful concept of a minimal diffusion. 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.
Original languageEnglish
Article number34
Pages (from-to)1-13
Number of pages13
JournalElectronic Communications in Probability
Volume19
DOIs
Publication statusPublished - 11 Jun 2014

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