Central limit theorem in the space D[0,1]
Sufficient conditions for the validity of the central limit theorem for series in D[0,1] are given. This result is applied in order to give a new proof of the invariance principle in the form given by \textit{J. Jurečková} [J. Math. Operationsforsch. Stat., Ser. Stat. 11, 61-73 (1980; Zbl 0441.62037)]. Sufficient conditions for the weak convergence of independent identically distributed normed random elements from D[0,1] to a stable process are also given.
scientific article; zbMATH DE number 3953952