What is the condition for ergodicity, weakly mixing, and strongly mixing properties of Gaussian process in terms of its spectrum?
In a similar way let us consider a stationary vector valued Gaussian process indexed by an infinite discrete abelian group with mean zero. What is the condition of ergodicity of such a process in terms of its spectral measure?
I apologize if this question is not of mathoverflow standard. I am not an expert of this subject. But I need to learn some points in this matter urgently. So can someone please suggest me some reference books on stationary stochastic process, and stationary Gaussian process, which starts from basic theorems and goes (perhaps) upto the state of art on this subject?
Advanced thanks for any suggestion, comment, and etc.