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The invariance principle for Banach space valued random variables

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  • Kuelbs, J.

Abstract

We extend the invariance principle to triangular arrays of Banach space valued random variables, and as an application derive the invariance principle for lattices of random variables. We also point out how the q-dimensional time parameter Yeh-Wiener process is naturally related to a one dimensional time Wiener process with an infinite dimensional Banach space as a state space.

Suggested Citation

  • Kuelbs, J., 1973. "The invariance principle for Banach space valued random variables," Journal of Multivariate Analysis, Elsevier, vol. 3(2), pages 161-172, June.
    • Handle: RePEc:eee:jmvana:v:3:y:1973:i:2:p:161-172
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    Cited by:

    1. István Berkes & Robertas Gabrys & Lajos Horváth & Piotr Kokoszka, 2009. "Detecting changes in the mean of functional observations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(5), pages 927-946, November.
    2. Jürgen Dippon & Harro Walk, 2006. "The Averaged Robbins – Monro Method for Linear Problems in a Banach Space," Journal of Theoretical Probability, Springer, vol. 19(1), pages 166-189, January.
    3. Michael Messer, 2022. "Bivariate change point detection: Joint detection of changes in expectation and variance," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 886-916, June.
    4. Florence Merlevède, 2003. "On the Central Limit Theorem and Its Weak Invariance Principle for Strongly Mixing Sequences with Values in a Hilbert Space via Martingale Approximation," Journal of Theoretical Probability, Springer, vol. 16(3), pages 625-653, July.
    5. Dedecker, Jérôme & Merlevède, Florence, 2003. "The conditional central limit theorem in Hilbert spaces," Stochastic Processes and their Applications, Elsevier, vol. 108(2), pages 229-262, December.
    6. Fremdt, Stefan & Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef G., 2014. "Functional data analysis with increasing number of projections," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 313-332.
    7. Alfredas Račkauskas & Charles Suquet, 2004. "Necessary and Sufficient Condition for the Functional Central Limit Theorem in Hölder Spaces," Journal of Theoretical Probability, Springer, vol. 17(1), pages 221-243, January.

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