A uniform law for convergence to the local times of linear fractional stable motions

Preprint, Other literature type English OPEN
Duffy, James A.;
  • Publisher: The Institute of Mathematical Statistics
  • Journal: issn: 1050-5164
  • Publisher copyright policies & self-archiving
  • Related identifiers: doi: 10.1214/14-AAP1085
  • Subject: 60J55 | integral functionals of stochastic processes | 62M10 | 60F17 | 62G08 | 60G18 | nonlinear cointegration | Mathematics - Statistics Theory | nonparametric regression | Fractional stable motion | fractional Brownian motion | weak convergence to local time | local time

We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the ... View more
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    if H = 1/α,

    Lemma 9.4. n cs ds−1 . X ds−1 . ndn−1 = en,

    s=k+1 ck+s s=1

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