I know of the typical martingale convergence theorem, doob convergence theorem etc, but they mostly pertain to a.s. convergence. Are there any theorems that prove a martingale $M_n \rightarrow M$ with distribution? I understand all the a.s. theorems apply for convergence in distribution, but I am after theorems that only converge in distribution
2026-04-03 03:36:14.1775187374
Are there any convergence in distribution (weak convergence) theorems related to martingales?
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The martingale CLT: https://en.wikipedia.org/wiki/Martingale_central_limit_theorem might be what you are after?