Geodesic
Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 112-128

Voir la notice de l'article provenant de la source Numdam

We study the partial differential equation         max{Lu - f, H(Du)} = 0 where u is the unknown function, L is a second-order elliptic operator, f is a given smooth function and H is a convex function. This is a model equation for Hamilton-Jacobi-Bellman equations arising in stochastic singular control. We establish the existence of a unique viscosity solution of the Dirichlet problem that has a Hölder continuous gradient. We also show that if H is uniformly convex, the gradient of this solution is Lipschitz continuous.

DOI : 10.1051/cocv/2012001
Classification : 35J15, 49L25, 35R35, 49L20
Keywords: HJB equation, gradient constraint, free boundary problem, singular control, penalty method, viscosity solutions 
@article{COCV_2013__19_1_112_0,
     author = {Hynd, Ryan},
     title = {Analysis of {Hamilton-Jacobi-Bellman} equations arising in stochastic singular control},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {112--128},
     publisher = {EDP-Sciences},
     volume = {19},
     number = {1},
     year = {2013},
     doi = {10.1051/cocv/2012001},
     mrnumber = {3023063},
     zbl = {1259.49043},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012001/}
}
TY  - JOUR
AU  - Hynd, Ryan
TI  - Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2013
SP  - 112
EP  - 128
VL  - 19
IS  - 1
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012001/
DO  - 10.1051/cocv/2012001
LA  - en
ID  - COCV_2013__19_1_112_0
ER  - 
%0 Journal Article
%A Hynd, Ryan
%T Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2013
%P 112-128
%V 19
%N 1
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2012001/
%R 10.1051/cocv/2012001
%G en
%F COCV_2013__19_1_112_0
Hynd, Ryan. Analysis of Hamilton-Jacobi-Bellman equations arising in stochastic singular control. ESAIM: Control, Optimisation and Calculus of Variations, Tome 19 (2013) no. 1, pp. 112-128. doi: 10.1051/cocv/2012001

Cité par Sources :