Abstract
This paper considers Darlin-Erdős theorems for sums of martingale differences. Our main theorem provides an optimal result for the case of bounded martingale difference sequences. A number of other results are presented, which deal with the unbounded case and which specialize to the case of independent summands. Previous related work on this problem has been based on deep strong approximation theorems. One of the novel features of our approach is that our methods rely on the more easily accessible Skorokhod-type embeddings.
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Einmahl, U., Mason, D.M. Darling-Erdős theorems for martingales. J Theor Probab 2, 437–460 (1989). https://doi.org/10.1007/BF01051877
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DOI: https://doi.org/10.1007/BF01051877