Abstract
It is well-known that a Markov kernel P from a space T to a space X can be represented by a random mapping, i.e. by a probability measure μ on the space of mappings f:T→X. Assuming T and X to carry a (partial or total) ordering, this paper studies under what conditions the measure μ may be restricted to order-preserving mappings f. Reformulated as a marginal problem: given a family of distributions μt, t ∈ T, on X, when does there exist a measure μ as above having these distributions as its marginals.
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© 1997 Springer Science+Business Media Dordrecht
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Kellerer, H.G. (1997). Representation of Markov Kernels by Random Mappings under Order Conditions. In: Beneš, V., Štěpán, J. (eds) Distributions with given Marginals and Moment Problems. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5532-8_18
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DOI: https://doi.org/10.1007/978-94-011-5532-8_18
Publisher Name: Springer, Dordrecht
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