This paper is concerned with the generalized principal eigenvalue for Hamilton–Jacobi–Bellman (HJB) equations arising in a class of stochastic ergodic control. We give a necessary and sufficient condition so that the generalized principal eigenvalue of an HJB equation coincides with the optimal value of the corresponding ergodic control problem. We also investigate some qualitative properties of the generalized principal eigenvalue with respect to a perturbation of the potential function.
Mots-clés : Principal eigenvalue, Hamilton–Jacobi–Bellman equation, Ergodic control, Recurrence and transience
@article{AIHPC_2015__32_3_623_0, author = {Ichihara, Naoyuki}, title = {The generalized principal eigenvalue for {Hamilton{\textendash}Jacobi{\textendash}Bellman} equations of ergodic type}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {623--650}, publisher = {Elsevier}, volume = {32}, number = {3}, year = {2015}, doi = {10.1016/j.anihpc.2014.02.003}, mrnumber = {3353703}, zbl = {1322.35142}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2014.02.003/} }
TY - JOUR AU - Ichihara, Naoyuki TI - The generalized principal eigenvalue for Hamilton–Jacobi–Bellman equations of ergodic type JO - Annales de l'I.H.P. Analyse non linéaire PY - 2015 SP - 623 EP - 650 VL - 32 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2014.02.003/ DO - 10.1016/j.anihpc.2014.02.003 LA - en ID - AIHPC_2015__32_3_623_0 ER -
%0 Journal Article %A Ichihara, Naoyuki %T The generalized principal eigenvalue for Hamilton–Jacobi–Bellman equations of ergodic type %J Annales de l'I.H.P. Analyse non linéaire %D 2015 %P 623-650 %V 32 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2014.02.003/ %R 10.1016/j.anihpc.2014.02.003 %G en %F AIHPC_2015__32_3_623_0
Ichihara, Naoyuki. The generalized principal eigenvalue for Hamilton–Jacobi–Bellman equations of ergodic type. Annales de l'I.H.P. Analyse non linéaire, Tome 32 (2015) no. 3, pp. 623-650. doi : 10.1016/j.anihpc.2014.02.003. http://www.numdam.org/articles/10.1016/j.anihpc.2014.02.003/
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