Probability bounds for M-Skorohod oscillations
Taqqu, Murrad S.
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Citation (published version)F AVRAM, MS TAQQU. 1989. "Probability Bounds for M-Skorohod Oscillations" Stochastic Processes and their Applications, Volume 33, Issue 1, pp. 63 - 72 (10). https://doi.org/10.1016/0304-4149(89)90066-5
Billingsley developed a widely used method for proving weak convergence with respect to the sup-norm and J -Skorohod topologies, once convergence of the finite-dimensional distributions has been established. 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.
Originally published as a Technical Report 1 Oct 86-30 Sep 1987, for North Carolina Univ At Chapel Hill Center For Stochastic Processes. Source: Defense Technical Information Center: http://www.dtic.mil/docs/citations/ADA187981