Hamadouche, D. Invariance principles in Hölder spaces. (English) Zbl 0965.60011 Port. Math. 57, No. 2, 127-151 (2000). The weak convergence of random elements in Hölder space \(H_\alpha[0,1]\) is studied, especially in a separable subspace \(H^0_\alpha\) of functions \(f\), for which the Hölderian modulus of continuity \(\omega_\alpha (f, \delta)\to 0\), as \(\delta\to 0\). J. Lamperti [Trans. Am. Math. Soc. 104, 430-435 (1962; Zbl 0113.33502)] established a Hölderian version of i.i.d. Donsker-Prokhorov’s invariance principle. In the present paper it is extended to the cases of strong mixing and of associated random variables, see the moment inequalities for the latter of T. Birkel [Ann. Probab. 16, No. 3, 1184-1193 (1988; Zbl 0647.60039)]. Similar convergence is proved for the convolution smoothing of partial sums processes. The presentation is very clear. Some proofs of auxiliary statements are given, which are known in the literature. Reviewer: Oleksandr Kukush (Kiev) Cited in 1 ReviewCited in 10 Documents MSC: 60B10 Convergence of probability measures 60F05 Central limit and other weak theorems 60F17 Functional limit theorems; invariance principles 62G30 Order statistics; empirical distribution functions Keywords:Hölder space; invariance principle; strong mixing; tightness of measures Citations:Zbl 0113.33502; Zbl 0647.60039 PDF BibTeX XML Cite \textit{D. Hamadouche}, Port. Math. 57, No. 2, 127--151 (2000; Zbl 0965.60011) Full Text: EuDML OpenURL