### Abstract

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 language | English |
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Pages (from-to) | 307-309 |

Number of pages | 3 |

Journal | Statistics and Probability Letters |

Volume | 9 |

Issue number | 4 |

DOIs | |

State | Published - Apr 1990 |

### Keywords

- Skorokhod as construction
- conditional distributions
- stochastic differential equation

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## Cite this

Rachev, S. T., & Rüschendorf, L. (1990). A counterexample to A.S. constructions.

*Statistics and Probability Letters*,*9*(4), 307-309. https://doi.org/10.1016/0167-7152(90)90137-V