LAW OF LARGE NUMBERS FOR MONOTONE CONVOLUTION
Jiun-Chau Wang
Enzo Wendler
Abstract: Using the martingale convergence theorem, we prove a law of large numbers for
monotone convolutions , where ’s are probability laws on with
finite variances but not required to be iden-tical.
2000 AMS Mathematics Subject Classification: Primary: 46L53; Secondary: 60F05,
60J05.
Keywords and phrases: Monotone convolution, Markov chains, martingale, law of large
numbers.