Abstract
In this paper it is shown that every invariance principle of probability theory is equivalent to a nonstandard construction of internal S-continuous processes, which all represent — up to an infinitesimal error — the limit process. This can be applied e.g. to obtain Anderson’s nonstandard construction of a Brownian motion on a hyperfinite set.
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© 1995 Springer Science+Business Media Dordrecht
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Landers, D., Rogge, L. (1995). Nonstandrad Characterization for a General Invariance Principle. In: Albeverio, S.A., Luxemburg, W.A.J., Wolff, M.P.H. (eds) Advances in Analysis, Probability and Mathematical Physics. Mathematics and Its Applications, vol 314. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8451-7_15
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DOI: https://doi.org/10.1007/978-94-015-8451-7_15
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