Consider a white noise process $x(t)$ defined by the Dirac Delta function $\delta$, were
$$cov(x(t),x(t_1))=\delta(t-t_1)$$
What is the variance of this noise process ? We have that $$cov(x(t),x(t))=\delta(t-t)=\delta(t-t)=+\infty$$but I know the dirac delta is a heuristic function and I was wondering if the variance is defined differently, since I saw in a paper that they claim the variance here is 1.