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Monotone bivariate Markov kernels with specified marginals
Author(s):
Motoya
Machida;
Alexander
Shibakov
Journal:
Proc. Amer. Math. Soc.
138
(2010),
2187-2194.
MSC (2010):
Primary 60E15;
Secondary 62E15, 60J05
Posted:
February 1, 2010
MathSciNet review:
2596058
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Additional information
Abstract:
Given two Markov kernels  and  on an ordered Polish space, such that  is stochastically dominated by  , we establish the existence of: (i) a monotone bivariate Markov kernel whose marginals are  and  and (ii) an upward coupler from  to  . 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
Email:
alex@math.tntech.edu
DOI:
10.1090/S0002-9939-10-10241-X
PII:
S 0002-9939(10)10241-X
Keywords:
Probability measures with given marginals,
stochastically monotone Markov kernel,
measurable selection,
coupling,
Fill's algorithm
Received by editor(s):
February 9, 2009,
Received by editor(s) in revised form:
October 5, 2009
Posted:
February 1, 2010
Communicated by:
Richard C. Bradley
Copyright of article:
Copyright
2010,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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