Triplet Markov chains (Q1854705)

Denote by \(X_n\) a hidden process that we estimate from an observed process \(Y_n\). When \(X_n\) has a finite set of values and \((X_n,Y_n)\) is Markov, recursive formulas may be used in computations, this is called the pairwise Markov chains model in previous works. Now, when \((X_n,Y_n)\) is not Markov, it may be that with additional information \(U_n\), some \((X_n,U_n,Y_n)\) is. If \(U_n\) also has a finite set of values the same formulas yield estimates for \((X_n,U_n)\), then for \(X_n\) after addition. The author names this the triplet Markov chain model.