A NEW CRITERIUM FOR THE ERGODICITY OF HAMILTON-JACOBI-BELLMAN TYPE EQUATIONS

Carlo Bianca (1) , Christian Dogbe (2)

1 LPTMC - Laboratoire de Physique Théorique de la Matière Condensée
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

This paper deals with the link among the large-time behavior of a class of fully nonlinear partial differential equations, the concept of mean ergodicity of a dynamical system and the controllability problem. Specifically Abelian-Tauberian arguments are employed to develop a theory for the analysis of the ergodic mean behavior of systems of degenerate elliptic-parabolic equations and general systems of vector fields satisfying Hörmander's condition. A new criterium for ergodicity is established which is based on an asymptotic estimation of the rate of convergence. The new criterium is employed for the asymptotic analysis of Hamilton-Jacobi-Bellman type equations .

Domaines: Equations aux dérivées partielles [math.AP]

Carlo Bianca, Christian Dogbe. A NEW CRITERIUM FOR THE ERGODICITY OF HAMILTON-JACOBI-BELLMAN TYPE EQUATIONS. Global and Stochastic Analysis, 2018, Vol. 5 (No. 2), pp.67-99. ⟨hal-02151728⟩