Joint convergence along different subsequences of the signed cubic variation of fractional Brownian motion

    Authors

    K. Burdzy; D. Nualart;J. Swanson

    Comments

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    Abbreviated Journal Title

    Probab. Theory Relat. Field

    Keywords

    Fractional Brownian motion; Cubic variation; Convergence in law; MULTIPLE STOCHASTIC INTEGRALS; CENTRAL LIMIT-THEOREMS; FUNCTIONALS; Statistics & Probability

    Abstract

    The purpose of this paper is to study the convergence in distribution of two subsequences of the signed cubic variation of the fractional Brownian motion with Hurst parameter . We prove that, under some conditions on both subsequences, the limit is a two-dimensional Brownian motion whose components may be correlated and we find explicit formulae for its covariance function.

    Journal Title

    Probability Theory and Related Fields

    Volume

    159

    Issue/Number

    1-2

    Publication Date

    1-1-2014

    Document Type

    Article

    Language

    English

    First Page

    237

    Last Page

    272

    WOS Identifier

    WOS:000335900500007

    ISSN

    0178-8051

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