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Finite, integrable and bounded time embeddings for diffusions
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Ankirchner, Stefan, Hobson, David (David G.) and Strack, Philipp (2015) Finite, integrable and bounded time embeddings for diffusions. Bernoulli, 21 (2). pp. 1067-1088. doi:10.3150/14-BEJ598 ISSN 1350-7265.
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Official URL: https://doi.org/10.3150/14-BEJ598
Abstract
We solve the Skorokhod embedding problem (SEP) for a general time-homogeneous diffusion X: given a distribution \rho, we construct a stopping time T such that the stopped process X_T has the distribution \rho? Our solution method makes use of martingale representations (in a similar way to Bass [3] who solves the SEP for Brownian motion) and draws on law uniqueness of weak solutions of SDEs.
Then we ask if there exist solutions of the SEP which are respectively finite almost surely, integrable or bounded, and when does our proposed construction have these properties. We provide conditions that guarantee existence of finite time solutions. Then, we fully characterize the distributions that can be embedded with integrable stopping times. Finally, we derive necessary, respectively sufficient, conditions under which there exists a bounded embedding.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||||
Journal or Publication Title: | Bernoulli | ||||||
Publisher: | Int Statistical Institute | ||||||
ISSN: | 1350-7265 | ||||||
Official Date: | 21 April 2015 | ||||||
Dates: |
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Volume: | 21 | ||||||
Number: | 2 | ||||||
Page Range: | pp. 1067-1088 | ||||||
DOI: | 10.3150/14-BEJ598 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Open Access (Creative Commons) | ||||||
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