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Weighted Approximations to Continuous Time Martingales with Applications |
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| Authors: | Erich Haeusler,& David M. Mason |
| Affiliation: | Universität Giessen,;Department of Mathematical Sciences, 501 Ewing Hall, University of Delaware, Newark, DE 19716, USA |
| 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. |
| Keywords: | uniform empirical distribution function uniform empirical process weighted approximation methodology weighted empirical process Wiener process |