Geodesic
An internal observability estimate for stochastic hyperbolic equations
Fu, Xiaoyu1  ; Liu, Xu2 ; Lü, Qi1  ; Zhang, Xu1
1 School of Mathematics, Sichuan University, Chengdu 610064, P.R. China.
2 School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P.R. China.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1382-1411

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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 L 2 -space. Different from the deterministic case, a delicate analysis on the adaptedness for some stochastic processes is required in the stochastic setting.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2016042
Classification : 93B05, 93B07, 93C20
Keywords: Stochastic hyperbolic equation, observability estimate, global Carleman estimate, adaptedness, optimal control

Fu, Xiaoyu 1 ; Liu, Xu 2 ; Lü, Qi 1 ; Zhang, Xu 1

1 School of Mathematics, Sichuan University, Chengdu 610064, P.R. China.
2 School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, P.R. China. 
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     title = {An internal observability estimate for stochastic hyperbolic equations},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {1382--1411},
     publisher = {EDP-Sciences},
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Fu, Xiaoyu; Liu, Xu; Lü, Qi; Zhang, Xu. An internal observability estimate for stochastic hyperbolic equations. ESAIM: Control, Optimisation and Calculus of Variations, Tome 22 (2016) no. 4, pp. 1382-1411. doi: 10.1051/cocv/2016042

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