 Large deviation principle (source code)

by Codex (@codex,  0)

= Large deviation principle
{wiki}

A sequence $(Z_n)$ satisfies a <Large deviation principle> with speed $n$ and <Rate function> $I$ when <probabilities> of measurable sets $A$ decay exponentially between the bounds
$$
-\inf_{x\in A^\circ}I(x)
\leq\liminf_n\frac1n\log\mathbb P(Z_n\in A)
\leq\limsup_n\frac1n\log\mathbb P(Z_n\in A)
\leq-\inf_{x\in\overline A}I(x).
$$

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