This paper is addressed to establishing an internal observability estimate for some linear stochastic hyperbolic equations. The key is to establish a new global Carleman estimate for forward stochastic hyperbolic equations in the -space. Different from the deterministic case, a delicate analysis on the adaptedness for some stochastic processes is required in the stochastic setting.
Accepted:
DOI: 10.1051/cocv/2016042
Mots-clés : Stochastic hyperbolic equation, observability estimate, global Carleman estimate, adaptedness, optimal control
@article{COCV_2016__22_4_1382_0, author = {Fu, Xiaoyu and Liu, Xu and L\"u, Qi and Zhang, Xu}, title = {An internal observability estimate for stochastic hyperbolic equations}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {1382--1411}, publisher = {EDP-Sciences}, volume = {22}, number = {4}, year = {2016}, doi = {10.1051/cocv/2016042}, zbl = {1350.93021}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/cocv/2016042/} }
TY - JOUR AU - Fu, Xiaoyu AU - Liu, Xu AU - Lü, Qi AU - Zhang, Xu TI - An internal observability estimate for stochastic hyperbolic equations JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2016 SP - 1382 EP - 1411 VL - 22 IS - 4 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/cocv/2016042/ DO - 10.1051/cocv/2016042 LA - en ID - COCV_2016__22_4_1382_0 ER -
%0 Journal Article %A Fu, Xiaoyu %A Liu, Xu %A Lü, Qi %A Zhang, Xu %T An internal observability estimate for stochastic hyperbolic equations %J ESAIM: Control, Optimisation and Calculus of Variations %D 2016 %P 1382-1411 %V 22 %N 4 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/cocv/2016042/ %R 10.1051/cocv/2016042 %G en %F COCV_2016__22_4_1382_0
Fu, Xiaoyu; Liu, Xu; Lü, Qi; Zhang, Xu. An internal observability estimate for stochastic hyperbolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Volume 22 (2016) no. 4, pp. 1382-1411. doi : 10.1051/cocv/2016042. http://archive.numdam.org/articles/10.1051/cocv/2016042/
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