Abstract
This paper uses a Martingale-like approach and establishes, among other things, the existence of continuous Gaussian processes with independent increments on those locally compact Abelian groups whose duals support corresponding continuous nonnegative quadratic forms.
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Bingham, M.S. Functional central limit theorems for approximate Martingale arrays in a locally compact Abelian group. J Theor Probab 1, 3–26 (1988). https://doi.org/10.1007/BF01076286
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DOI: https://doi.org/10.1007/BF01076286