An excercise question for time series analysis asks:

Consider the process
$$
y_t = 0.8y_{t-1} + 0.1y_{t-2} + u_t
$$

 1. Is this process weakly stationary (I would answer this with the stability triangle)

 2. Under which assumptions does this property imply strong stationarity

I thought that strong stationarity always implies weak stationarity, but not that it can be the other way around.