I have the following question:
The Markov process with two states and a transition matrix $$P =\begin{pmatrix} 0.3 & 0.7 \\ 0.3 & 0.7 \end{pmatrix}$$ has memory zero. Is it true?
My guess is that (this?) Markov process has memory $1$ because to predict for example something for the next step we can use the matrix $P$ which I suppose describes the process with two states. Am I correct? Could you please give me a better explanation of why a Markov process has memory $0$ or $1$ (or more eventually)?