Monotone bivariate Markov kernels with specified marginals
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- by Motoya Machida and Alexander Shibakov PDF
- Proc. Amer. Math. Soc. 138 (2010), 2187-2194 Request permission
Abstract:
Given two Markov kernels $k$ and $k’$ on an ordered Polish space, such that $k$ is stochastically dominated by $k’$, we establish the existence of: (i) a monotone bivariate Markov kernel whose marginals are $k$ and $k’$ and (ii) an upward coupler from $k$ to $k’$. This extends the results of Strassen, Kamae, Krengel and O’Brien to Markov kernels. Two examples are also given. The first is a simple illustration of our original motivation for this work, while the second demonstrates the optimality of our main result. The key technique is a combination of the standard probability/charge approach and the use of measurable selections of multivalued measurable maps.References
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Additional Information
- Motoya Machida
- Affiliation: Department of Mathematics, Tennessee Technological University, Cookeville, Tennessee 38505
- Email: mmachida@tntech.edu
- Alexander Shibakov
- Affiliation: Department of Mathematics, Tennessee Technological University, Cookeville, Tennessee 38505
- MR Author ID: 355084
- Email: alex@math.tntech.edu
- Received by editor(s): February 9, 2009
- Received by editor(s) in revised form: October 5, 2009
- Published electronically: February 1, 2010
- Communicated by: Richard C. Bradley
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 138 (2010), 2187-2194
- MSC (2010): Primary 60E15; Secondary 62E15, 60J05
- DOI: https://doi.org/10.1090/S0002-9939-10-10241-X
- MathSciNet review: 2596058