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Almost sure invariance principle

  1. Apr 13, 2015 #1
    I would like to understand the Almost Sure Invariance Principle:
    "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
  2. jcsd
  3. Apr 18, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
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