Fluctuations of the empirical quantiles of independent Brownian motions

    Authors

    J. Swanson

    Comments

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    Abbreviated Journal Title

    Stoch. Process. Their Appl.

    Keywords

    Quantile process; Order statistics; Fluctuations weak convergence; Fractional Brownian motion; Quartic variation; TAGGED PARTICLE; EXCLUSION; SYSTEM; Statistics & Probability

    Abstract

    We consider lid Brownian motions, B(j)(t), where B(j)(0) has a rapidly decreasing, smooth density function f. The empirical quantiles, or pointwise order statistics, are denoted by B(j:n)(t), and we consider a sequence Q(n)(t) = B(j(n):n) (t), where j (n)/n - > alpha is an element of (0, 1). This sequence converges in probability to q(t), the alpha-quantile of the law of B(j)(t). We first show convergence in law in C[0, infinity) of F(n) = n(1/2) (Q(n) - q). We then investigate properties of the limit process F, including its local covariance structure, and Holder-continuity and variations of its sample paths. In particular, we find that F has the same local properties as fBm with Hurst parameter H = 1/4. (C) 2010 Elsevier B.V. All rights reserved.

    Journal Title

    Stochastic Processes and Their Applications

    Volume

    121

    Issue/Number

    3

    Publication Date

    1-1-2011

    Document Type

    Article

    Language

    English

    First Page

    479

    Last Page

    514

    WOS Identifier

    WOS:000287223000005

    ISSN

    0304-4149

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