Weighted Approximations to Continuous Time Martingales with Applications

Erich Haeusler and David M. Mason

Scandinavian Journal of Statistics, 1999, vol. 26, issue 2, 281-295

Abstract: A weighted approximation to a sequence of continuous time martingales by a time transformed Wiener process is established. The basic tool of proof is the Skorohod imbedding for martingale difference sequences. As an application of the main result a useful weighted approximation to the randomly weighted uniform empirical process is derived. A number of other applications are also discussed.

Date: 1999
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