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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 33, Fasc. 2,
pages 225 - 231
 

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 μ ⊳μ ⊳...⊳μ 1 2 n , where μ j ’s are probability laws on ℝ 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.

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