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A New Criterion for Tightness of Stochastic Processes and an Application to Markov Processes

Erlenmaier, Ulrich

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Abstract

We prove a stochastic inequality for the modulus of continuity of a stochastic process U on the real line. It requires certain tail inequalities for the increments of U, refining a criterion of Billingsley (1968). Then this result is used to prove weak convergence of a goodness-of-fit test statistic for simple hypotheses about the conditional median function of a stationary Markovian time series.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 01 Jul 2016 07:03
Date: September 1997
Number of Pages: 16
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Schriftenreihe ID: Beiträge zur Statistik > Reports
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