For a class of Bellman equations in bounded domains we prove that sub-and supersolutions whose growth at the boundary is suitably controlled must be constant. The ellipticity of the operator is assumed to degenerate at the boundary and a condition involving also the drift is further imposed. We apply this result to stochastic control problems, in particular to an exit problem and to the small discount limit related with ergodic control with state constraints. In this context, our condition on the behavior of the operator near the boundary ensures some invariance property of the domain for the associated controlled diffusion process.
Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control / Bardi, M.; Cesaroni, A.; Rossi, L.. - In: ESAIM. COCV. - ISSN 1292-8119. - 22:3(2016), pp. 842-861. [10.1051/cocv/2015033]
Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control
Rossi L.
2016
Abstract
For a class of Bellman equations in bounded domains we prove that sub-and supersolutions whose growth at the boundary is suitably controlled must be constant. The ellipticity of the operator is assumed to degenerate at the boundary and a condition involving also the drift is further imposed. We apply this result to stochastic control problems, in particular to an exit problem and to the small discount limit related with ergodic control with state constraints. In this context, our condition on the behavior of the operator near the boundary ensures some invariance property of the domain for the associated controlled diffusion process.File | Dimensione | Formato | |
---|---|---|---|
Bardi_preprint_Nonexistence_2016.pdf
accesso aperto
Tipologia:
Documento in Pre-print (manoscritto inviato all'editore, precedente alla peer review)
Licenza:
Creative commons
Dimensione
312.7 kB
Formato
Adobe PDF
|
312.7 kB | Adobe PDF | |
Bardi_Nonexistence_2016.pdf
solo gestori archivio
Tipologia:
Versione editoriale (versione pubblicata con il layout dell'editore)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
353.29 kB
Formato
Adobe PDF
|
353.29 kB | Adobe PDF | Contatta l'autore |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.