English

Law of Large Numbers for Monotone Convolution

Functional Analysis 2013-04-05 v1

Abstract

Using martingale convergence theorem, we prove a law of large numbers for monotone convolutions μ1μ2μn\mu_{1}\triangleright\mu_{2}\triangleright\cdots\triangleright\mu_{n}, where μj\mu_{j}'s are probability laws on R\mathbb{R} with finite variances but not required to be identical.

Keywords

Cite

@article{arxiv.1304.1230,
  title  = {Law of Large Numbers for Monotone Convolution},
  author = {JC Wang and Enzo Wendler},
  journal= {arXiv preprint arXiv:1304.1230},
  year   = {2013}
}
R2 v1 2026-06-21T23:53:37.125Z