Weakly stationary Gaussian process?

1. Feb 20, 2012

aliirmak

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. Feb 20, 2012

sunjin09

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)