This paper is devoted to the study of the asymptotic behaviour of the value functions of both finite and infinite horizon stochastic control problems and to the investigation of their relationship with suitable stochastic ergodic control problems. Our methodology is based only on probabilistic techniques, as, for instance, the so-called randomisation of the control method, thus avoiding completely analytical tools from the theory of viscosity solutions. We are then able to treat with the case where the state process takes values in a general (possibly infinite-dimensional) real separable Hilbert space, and the diffusion coefficient is allowed to be degenerate.
Accepté le :
DOI : 10.1051/cocv/2018056
Mots-clés : Ergodic control, infinite-dimensional SDEs, BSDEs, randomisation of the control method
@article{COCV_2019__25__A12_0,
author = {Cosso, Andrea and Guatteri, Giuseppina and Tessitore, Gianmario},
title = {Ergodic control of infinite-dimensional stochastic differential equations with degenerate noise},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2018056},
zbl = {1437.60037},
mrnumber = {3959140},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2018056/}
}
TY - JOUR AU - Cosso, Andrea AU - Guatteri, Giuseppina AU - Tessitore, Gianmario TI - Ergodic control of infinite-dimensional stochastic differential equations with degenerate noise JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2018056/ DO - 10.1051/cocv/2018056 LA - en ID - COCV_2019__25__A12_0 ER -
%0 Journal Article %A Cosso, Andrea %A Guatteri, Giuseppina %A Tessitore, Gianmario %T Ergodic control of infinite-dimensional stochastic differential equations with degenerate noise %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2018056/ %R 10.1051/cocv/2018056 %G en %F COCV_2019__25__A12_0
Cosso, Andrea; Guatteri, Giuseppina; Tessitore, Gianmario. Ergodic control of infinite-dimensional stochastic differential equations with degenerate noise. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 12. doi : 10.1051/cocv/2018056. http://www.numdam.org/articles/10.1051/cocv/2018056/
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