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May 2015 Finite, integrable and bounded time embeddings for diffusions
Stefan Ankirchner, David Hobson, Philipp Strack
Bernoulli 21(2): 1067-1088 (May 2015). DOI: 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 $\tau$ such that the stopped process $X_{\tau}$ has the distribution $\rho$. Our solution method makes use of martingale representations (in a similar way to Bass (In Seminar on Probability XVII. Lecture Notes in Math. 784 (1983) 221–224 Springer) 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.

Citation

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Stefan Ankirchner. David Hobson. Philipp Strack. "Finite, integrable and bounded time embeddings for diffusions." Bernoulli 21 (2) 1067 - 1088, May 2015. https://doi.org/10.3150/14-BEJ598

Information

Published: May 2015
First available in Project Euclid: 21 April 2015

zbMATH: 1328.60101
MathSciNet: MR3338657
Digital Object Identifier: 10.3150/14-BEJ598

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

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Vol.21 • No. 2 • May 2015
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