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Law of Large Numbers for Monotone Convolution (1304.1230v1)
Published 4 Apr 2013 in math.FA
Abstract: Using martingale convergence theorem, we prove a law of large numbers for monotone convolutions $\mu_{1}\triangleright\mu_{2}\triangleright\cdots\triangleright\mu_{n}$, where $\mu_{j}$'s are probability laws on $\mathbb{R}$ with finite variances but not required to be identical.
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