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Transactions of the American Mathematical Society

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An almost sure invariance principle for Hilbert space valued martingales


Authors: Gregory Morrow and Walter Philipp
Journal: Trans. Amer. Math. Soc. 273 (1982), 231-251
MSC: Primary 60B12; Secondary 60F17
DOI: https://doi.org/10.1090/S0002-9947-1982-0664040-3
MathSciNet review: 664040
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Abstract: We obtain an almost sure approximation of a martingale with values in a real separable Hilbert space $ H$ by a suitable $ H$-valued Brownian motion.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1982-0664040-3
Keywords: Invariance principles, Hilbert space, martingales, law of the iterated logarithm, central limit theorem
Article copyright: © Copyright 1982 American Mathematical Society

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