Before revision:  When coupled with random initial policies, this value function takes closed-form expressions for polynomial and exponential costs, or for piecewise compositions of the latter, thus hinting in the most general case at the derivation of interval bounds for the value function in the form of power series or trigonometric sums.
After revision:  When coupled with random initial policies, this value function takes closed-form value functions for polynomial and exponential costs, or for piecewise compositions of the latter, thus hinting in the most general case at the derivation of interval bounds for the value function in the form of power series or trigonometric sums.