Optimal algebras of random-walk plans kindred to polynomial plans (Q1112526)

In the following every plan of random walk on the lattice of integers in \(R^ m\) whose polynomial algebra coincides with the algebra of the polynomial plan with the same stopping boundary will be called a polynomial-kindred (PK) plan. We find necessary and sufficient conditions for the completeness of PK plans and discuss the problem of optimal estimation based on incomplete plans. Moreover, we present a variant of the solution to the problem of choosing the best plan for the estimation of the main parameters in the case of plans for which the mean length of trajectories is uniformly bounded.