A counterexample to A.S. constructions

S. T. Rachev, L. Rüschendorf

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We discuss the question whether in Skorokhod's a.s. construction theorem for probability measures on a product space one can choose the second component of the a.s. convergent r.v.'s independent of n ε{lunate} N if the second marginals of the probability measures are independent of n ε{lunate}. It is, especially, shown by a counterexample that this is not true in general.

Original languageEnglish
Pages (from-to)307-309
Number of pages3
JournalStatistics and Probability Letters
Issue number4
StatePublished - Apr 1990


  • Skorokhod as construction
  • conditional distributions
  • stochastic differential equation


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