In this paper, we investigate a class of infinite-horizon optimal control problems for stochastic differential equations with delays for which the associated second order Hamilton−Jacobi−Bellman (HJB) equation is a nonlinear partial differential equation with delays. We propose a new concept for the viscosity solution including time t and identify the value function of the optimal control problems as a unique viscosity solution to the associated second order HJB equation.
Mots-clés : Second order Hamilton−Jacobi−Bellman equation, viscosity solution, infinite-horizon optimal control, stochastic differential equations with delays, existence and uniqueness
@article{COCV_2018__24_2_639_0,
author = {Zhou, Jianjun},
title = {A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated {HJB} equation},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {639--676},
publisher = {EDP-Sciences},
volume = {24},
number = {2},
year = {2018},
doi = {10.1051/cocv/2017042},
mrnumber = {3816408},
zbl = {1401.93234},
language = {en},
url = {http://archive.numdam.org/articles/10.1051/cocv/2017042/}
}
TY - JOUR AU - Zhou, Jianjun TI - A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2018 SP - 639 EP - 676 VL - 24 IS - 2 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2017042/ DO - 10.1051/cocv/2017042 LA - en ID - COCV_2018__24_2_639_0 ER -
%0 Journal Article %A Zhou, Jianjun %T A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %P 639-676 %V 24 %N 2 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2017042/ %R 10.1051/cocv/2017042 %G en %F COCV_2018__24_2_639_0
Zhou, Jianjun. A class of infinite-horizon stochastic delay optimal control problems and a viscosity solution to the associated HJB equation. ESAIM: Control, Optimisation and Calculus of Variations, Tome 24 (2018) no. 2, pp. 639-676. doi : 10.1051/cocv/2017042. http://archive.numdam.org/articles/10.1051/cocv/2017042/
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