Resonance phenomena for second-order stochastic control equations

Patricio Felmer (1) , Alexander Quaas (2) , Boyan Sirakov (3, 4)

1 DIM - Departamento de Ingenieria Matematica and Centro de Modelamiento Matematico
2 Departamento de Matematica [Valparaiso]
3 MODAL'X - Modélisation aléatoire de Paris X
4 CAMS - Centre d'Analyse et de Mathématique sociales

We study the solvability and the properties of the set of solutions to the Dirichlet problem for a uniformly elliptic second order Hamilton-Jacobi-Bellman operator, with respect to the sign of its two principal eigenvalues. We are in particular interested in the "resonance" cases, when one of the eigenvalues is zero. We also obtain a new uniqueness result for a operator with negative eigenvalues.

Domaines: Equations aux dérivées partielles [math.AP]

Patricio Felmer, Alexander Quaas, Boyan Sirakov. Resonance phenomena for second-order stochastic control equations. SIAM Journal on Mathematical Analysis, 2010, 42 (3), pp.997-1024. ⟨hal-00351673v2⟩