Probability Theory and Related Fields

, Volume 88, Issue 3, pp 381–404 | Cite as

Nearby variables with nearby conditional laws and a strong approximation theorem for Hilbert space valued martingales

  • Ditlev Monrad
  • Walter Philipp


In this paper we focus on sequences of random vectors which do not admit a strong approximation of their partial sums by sums of independent random vectors. In the first part we prove conditional versions of the Strassen-Dudley theorem. We apply these in the second part of the paper to obtain strong invariance principles for vector-valued martingales which, when properly normalized, converge in law to a mixture of Gaussian distributions.


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Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • Ditlev Monrad
    • 1
  • Walter Philipp
    • 1
  1. 1.Departments of Mathematics and StatisticsUniversity of IllinoisUrbanaUSA

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