I am trying to understand and prove the statement:

The normal (or Gaussian) process is stationary in the wide sense if and only if it is strictly stationary.

I know the following:

1. A strictly stationary process is also stationary in the wide sense if ${E}[x_t^2] < \infty$
2. For a Gaussian process, the entire distribution is determined by the mean and covariance function, making it unique in terms of properties of stationarity.

However, I am struggling with how to formally show this equivalence for Gaussian processes.

Could someone guide me through the proof or provide insights into why this equivalence holds in the Gaussian case?

Thank you!