https://dudusoar.github.io/tags/convergence-in-probability/Recent content in Convergence in Probability on Yuchen DuHugo -- 0.164.0en-usFri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/17-expectation-variance-proof-route/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/17-expectation-variance-proof-route/Expanding the recursion explains how initial error and historical noise decay, but usually yields convergence in probability rather than almost-sure convergence.https://dudusoar.github.io/posts/stochastic-approximation/21-why-mean-square-analysis-stops-at-probability/Fri, 17 Jul 2026 00:00:00 +0000https://dudusoar.github.io/posts/stochastic-approximation/21-why-mean-square-analysis-stops-at-probability/Vanishing expectation and variance control each time slice, but they do not directly control the shape of an infinite sample path.