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Homework Help: Weakly stationary Gaussian process?

  1. Feb 20, 2012 #1
    X = (Y(t))^2 where Y(t) is zero mean Gaussian process and correlation function R_YY = exp(-λ|τ|)
    i want to check if X is weakly stationary.

    So i guess for the first part, i checked if mean is constant
    σ^2=R_YY = exp(-λ|0|) = 1
    E(X^2) = μ^2+ σ^2 = 1 since μ is zero and σ = 1

    I wanted to check if auto-correlation is a function of τ. But I am pretty badly stuck at finding auto-correlation of X. How should i proceed?
  2. jcsd
  3. Feb 20, 2012 #2
    Since Y(t) is Gaussian process, the joint distribution of Y(t1) and Y(t2) are totally determined by R_YY(t1-t2), which is a function of tau=t1-t2, therefore everything about Y(t1) and Y(t2) should at most be a function of tau (the mean and variance are constant functions of tau)
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