8 problems

Let $cmathcal{E}_cperp$ be the natural orthogonal-complement effective subspace defined above, and let $coverline{\bm p}$ be the vector defined in Corollary corresponding to…

Let $(X_k,Y_k)_{k\,in\mathbb{Z}}$ be a stationary infinite-dimensional hidden Markov model as in Section 3, with $X_k\in\{-1,1\}^{\mathbb{Z}}$ and $Y_k\in\{-1,1\}^{\mathbb{Z}}$. Su…

Greedy threshold-policy conjecture. The greedy policy is always a threshold policy.

Threshold-policy entropy optimality conjecture. In the special case, the infimum of entropy attainable under threshold policies is the same as that under general policies.

Ergodicity conjecture. The conditions of that theorem can be weakened to the case when the underlying chain is only ergodic.

Kunita's exchange conjecture. If the hidden process is purely nondeterministic and the observations are nondegenerate, then $$ holds true.

Let $\mathbf{f}_{n,l}$ be the unconstrained hidden Markov model with $l$ hidden states and strings of length $n$, and let $d(n,l)$ denote the maximum degree of its invariants. Mono…

Let $\Sigma$ be the alphabet, let $\mathbf{g}_{n,d}$ denote the parameterization of the relevant hidden Markov model, and let $p=(p(v))_{v\in\Sigma^n}$ be a string function. For wo…