Covariance matrix of infinite normal random variables

Question

Lets say that X is a normally distributed random variable with $\sigma_X = \lim_{a\to\infty} a$ and $E[X] = 0$. Lets say that Y is a normally distributed random variable with $\sigma_Y = \lim_{a\to\infty} 1/a$ and $E[Y] = 0$. What is the joint distribution covariance matrix of X and Y.