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On Asymptotic Proximity of Distributions

Author

Listed:
  • Youri Davydov

    (Université de Lille I–Bat. M2)

  • Vladimir Rotar

    (San Diego State University
    Russian Academy of Sciences)

Abstract

We consider some general facts concerning the convergence $$P_{n}-Q_{n}\rightarrow0\quad\mbox{as}\ n\rightarrow\infty,$$ where P n and Q n are probability measures in a complete separable metric space. The main point is that the sequences {P n } and {Q n } are not assumed to be tight. We compare different possible definitions of the above convergence and establish some general properties.

Suggested Citation

  • Youri Davydov & Vladimir Rotar, 2009. "On Asymptotic Proximity of Distributions," Journal of Theoretical Probability, Springer, vol. 22(1), pages 82-98, March.
    • Handle: RePEc:spr:jotpro:v:22:y:2009:i:1:d:10.1007_s10959-008-0178-2
    DOI: 10.1007/s10959-008-0178-2
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    References listed on IDEAS

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    1. Rotar', V. I., 1979. "Limit theorems for polylinear forms," Journal of Multivariate Analysis, Elsevier, vol. 9(4), pages 511-530, December.
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