A strong invariance principle for reverse martingales (Q1077076)

A Skorokhod embedding of reverse martingales \(\{S_ n\}\) in Brownian motion given previously by \textit{D. J. Scott} and the author [Bull. Aust. Math. Soc. 27, 443-459 (1983; Zbl 0508.60043)] is sharpened. This theorem is then used to provide integral tests for upper and lower functions of \(S_ n\) and \(M_ n=\max_{1\leq i\leq n}| S_ i|.\) The results of the paper complement the corresponding results for martingales obtained by \textit{N. C. Jain}, \textit{K. Jogdeo} and \textit{W. F. Stout} [Ann. Probab. 3, 119-145 (1975; Zbl 0301.60026)].