I would like to understand the Almost Sure Invariance Principle:(adsbygoogle = window.adsbygoogle || []).push({});

"We say that the functions f_i: [a,b] →ℝ satisfy the Almost Sure Invariance Principle with error exponent γ < 1/2 if there are a probability space supporting a Brownian motion B and a sequence ξ_i, i ≥ 1, such that

(1) {f_i}_{i≥1} and {ξ_i}_{i≥1} have the same distribution;

(2) |B(n) - ∑_{i=1}^{n} (ξ_i)| < O(n^γ)

almost surely as n → ∞."

If anyone can give me an interpretation, I'll be very grateful

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# Almost sure invariance principle

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