Abstract
Weak convergence of martingales with values in Hilbert space is studied in the paper. Necessary and sufficient conditions for the convergence to Gaussian martingale with continuous trajectories are obtained.
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Submitted by A. I. Volodin
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Lavrentyev, V.V., Nazarov, L.V. A functional central limit theorem for Hilbert-valued martingales. Lobachevskii J Math 37, 138–145 (2016). https://doi.org/10.1134/S1995080216020086
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DOI: https://doi.org/10.1134/S1995080216020086