Lithuanian Mathematical Journal

, Volume 48, Issue 2, pp 212–227 | Cite as

Convergence in law of partial sum processes in p-variation norm



Let X 1, X 2, … be a sequence of independent identically distributed real-valued random variables, S n be the nth partial sum process S n (t) ≔ X 1 + ⋯ X tn, t ∈ [0, 1], W be the standard Wiener process on [0, 1], and 2 < p < ∞. It is proved that n −1/2 S n converges in law to σW as n → ∞ in p-variation norm if and only if EX 1 = 0 and σ 2 = EX 1 2 < ∞. The result is applied to test the stability of a regression model.


partial sum processes p-variation convergence in law nonlinear regression 


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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Institute of Mathematics and InformaticsVilniusLithuania
  2. 2.Department of Econometrical AnalysisVilnius UniversityVilniusLithuania

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