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High Dimensional Probability II pp 223–245Cite as

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A New Way to Obtain Estimates in the Invariance Principle

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Part of the book series: Progress in Probability ((PRPR,volume 47))

Abstract

This paper presents a new simple method of obtaining estimates on rates of convergence in the invariance principle, which may be used in arbitrary separable linear spaces. This method is applied to one-dimensional and infinite dimensional martingales, among other examples.

This research is partially supported by the Grant of RFFI: 99-01-00561 and by the Grant of INTAS: 98-1625.

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Author information

Authors and Affiliations

  1. Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa Av. Michoacán y la Purísima s/n, Col. Vicentina, 09340, México, D.F., Mexico

    Alexander I. Sakhanenko

Authors
  1. Alexander I. Sakhanenko
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Editor information

Editors and Affiliations

  1. Departments of Mathematics & Statistics, University of Connecticut, Storrs, CT, 06269, USA

    Evarist Giné

  2. Department of Statistics, University of Washington, Seattle, WA, 98195, USA

    Jon A. Wellner

  3. Department of Food and Resource Econ., University of Delaware, Newark, DE, 19717, USA

    David M. Mason

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Sakhanenko, A.I. (2000). A New Way to Obtain Estimates in the Invariance Principle. In: Giné, E., Mason, D.M., Wellner, J.A. (eds) High Dimensional Probability II. Progress in Probability, vol 47. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1358-1_15

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  • DOI: https://doi.org/10.1007/978-1-4612-1358-1_15

  • Publisher Name: Birkhäuser, Boston, MA

  • Print ISBN: 978-1-4612-7111-6

  • Online ISBN: 978-1-4612-1358-1

  • eBook Packages: Springer Book Archive

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