Consider $X_1$ discrete with finite alphabet $\mathcal{X_1}$. A chain of deterministic functions $f_i: \mathcal{X}_1 \rightarrow \mathcal{X}_{i+1}$ for $i=1, \dots, N$ identifies a Markov chain $X_1 \rightarrow X_2 \rightarrow \dotsc \rightarrow X_{N+1}$. However, the inverse chain $X_{N+1} \rightarrow \dotsc \rightarrow X_1$ is also a Markov chain due to the symmetry in the Markov condition. Can we identify a chain of function for this inverse chain? Or is the inverse chain necessarily based on non-determinist functions?
Asked
Active
Viewed 85 times
