convergence in distribution

依分布收敛

Probability · Undergraduate · Mathematics Resources editorial compilation (AI-assisted)

Other names / variants: weak convergence of probability laws

Translation evidence: Literature usage

Meaning in context

Real-valued laws converge in distribution when their CDFs converge to the limiting CDF at all its continuity points.

实数概率分布的分布函数在极限分布函数的每个连续点上收敛。

Example

If $Z$ is a fair sign, $(-1)^n Z$ has the same law for all $n$ and thus converges in distribution to that law, while its paths alternate.

Usage and distinctions

The variables need not share a probability space; continuity points are essential when the limiting law has atoms.

Read the encyclopedia explanation

Recommended reading in this subject · Preparation & skip guidance

Definition sources

1. Rick Durrett — Probability: Theory and Examples, fifth edition§3.2 Weak Convergence, opening definition · Checked 2026-10-14

Translation sources

1. 李东风 — 应用随机过程（北京大学）§1.4 收敛性，定义1.14(4) · Checked 2026-10-14

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