Blanc, Antoni Sintes Fluctuation inequalities with applications to convergence and regularity of stochastic processes indexed by \([0,1]^ q\). (English) Zbl 0615.60005 Publ., Secc. Mat., Univ. Autòn. Barc. 29, No. 1, 83-105 (1985). In the paper multiparameter stochastic processes with independent increments are considered. Some fluctuation inequalities for such processes extending those of P. J. Bickel and M. J. Wichura [Ann. Math. Stat. 42, 1656-1670 (1971; Zbl 0265.60011)] are obtained. These results are applied to prove some weak convergence and tightness theorems in the space \(D[0,1]^ q\) and to get a corresponding regularity condition. Reviewer: R.Morkvėnas MSC: 60B10 Convergence of probability measures 60G17 Sample path properties 60F05 Central limit and other weak theorems Keywords:multiparameter stochastic processes with independent increments; fluctuation inequalities; weak convergence; tightness theorems Citations:Zbl 0265.60011 PDFBibTeX XMLCite \textit{A. S. Blanc}, Publ., Secc. Mat., Univ. Autòn. Barc. 29, No. 1, 83--105 (1985; Zbl 0615.60005)