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Probability bounds for M-Skorohod oscillations
Murad S. Taqqu
Billingsley developed a widely used method for proving weak
convergence with respect to the sup-norm and
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.