Conditional convex orders and measurable martingale couplings

Lasse Leskelä, Matti Vihola

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)

Abstract

Strassen's classical martingale coupling theorem states that two real-valued random variables are ordered in the convex (resp. increasing convex) stochastic order if and only if they admit a martingale (resp. submartingale) coupling. By analyzing topological properties of spaces of probability measures equipped with a Wasserstein metric and applying a measurable selection theorem, we prove a conditional version of this result for real-valued random variables conditioned on a random element taking values in a general measurable space. We also provide an analogue of the conditional martingale coupling theorem in the language of probability kernels and illustrate how this result can be applied in the analysis of pseudo-marginal Markov chain Monte Carlo algorithms.
Original languageEnglish
Pages (from-to)2784-2807
Number of pages24
JournalBernoulli
Volume23
Issue number4A
DOIs
Publication statusPublished - 2017
MoE publication typeA1 Journal article-refereed

Keywords

  • Conditional coupling
  • Convex stochastic order
  • Increasing convex stochastic order
  • Martingale coupling
  • Pointwise coupling
  • Probability kernel

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