Abstract:
 It is known that there is a particular value, called critical value, for the ergodic type Bellman equation of first order. The critical value can be considered to be a first order counterpart of the principal eigenvalue of the second order linear differential operators. In this talk, we shall make some remarks on the representation of the critical value by the Lagrangian formulation in Euclidean space, which is often studied on compact spaces in dynamical systems. A connection to another representation motivated from the large deviation theory will be discussed in a formal way.
