Probability bounds for M-Skorohod oscillations

Florin Avram and Murad S. Taqqu

Stochastic Processes and their Applications, 1989, vol. 33, issue 1, 63-72

Abstract: Billingsley developed a widely used method for proving weak convergence with respect to the sup-norm and J1-Skorohod topologies, once convergence of the finite-dimensional distributions has been established. Here we show that Billingsley's method works not only for J oscillations, but also for M oscillations. This is done by identifying a common property of the J and M functions, called sub-triadditivity, and then showing that Billingsley's approach in the case of the J function can be adequately modified to apply to any sub-triadditive function.

Keywords: weak; convergence; Skorohod; topologies; sub-triadditivity (search for similar items in EconPapers)
Date: 1989
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