跳转至

依概率收敛

\(X_1\)\(X_2\)\(\cdots\)\(X_n\)\(\cdots\)随机变量序列,\(X\) 是随机变量,如果 \(\forall \varepsilon > 0\),有

\[ \lim_{n \to \infty} P \left ( \left | X_n - X \right | \ge \varepsilon \right ) = 0 \]

则称随机变量序列 \(\{ X_n \}\) 依概率收敛于 \(X\),记为

\[ X_n \overset{P}{\longrightarrow} X, \ n \to \infty \]