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Fluctuation inequalities with applications to convergence and regularity of stochastic processes indexed by \([0,1]^ q\). (English) Zbl 0615.60005

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

Citations:

Zbl 0265.60011
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