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6 MODES OF STOCHASTIC CONVERGENCE

A sequence of random variables can approach a limit in more than one sense, and the senses are genuinely different. Four are in standard use. This section defines them, establishes which implies which, and — what matters as much — gives an example showing that each converse fails.

6.1 The Four Definitions
6.2 The Hierarchy
6.3 Every Converse Fails
6.4 Practice Problems

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