In this Note, we present a Carleman inequality for linear backward stochastic parabolic equations (BSPEs) with general coefficients, and its applications in the observability of BSPEs, and in the null controllability of forward stochastic parabolic equations with general coefficients.
Dans cette Note, nous présentons une inégalité de Carleman pour les équations linéaires stochastiques paraboliques rétrogradés avec coefficients généraux, et ses applications à l'observabilité des équations stochastiques paraboliques rétrogradés avec coefficients généraux, et à la contrôlabilité nulle des équations stochastiques paraboliques progressives avec coefficients généraux.
Accepted:
Published online:
Shanjian Tang 1; Xu Zhang 2, 3
@article{CRMATH_2004__339_11_775_0, author = {Shanjian Tang and Xu Zhang}, title = {Carleman inequality for backward stochastic parabolic equations with general coefficients}, journal = {Comptes Rendus. Math\'ematique}, pages = {775--780}, publisher = {Elsevier}, volume = {339}, number = {11}, year = {2004}, doi = {10.1016/j.crma.2004.09.036}, language = {en}, }
TY - JOUR AU - Shanjian Tang AU - Xu Zhang TI - Carleman inequality for backward stochastic parabolic equations with general coefficients JO - Comptes Rendus. Mathématique PY - 2004 SP - 775 EP - 780 VL - 339 IS - 11 PB - Elsevier DO - 10.1016/j.crma.2004.09.036 LA - en ID - CRMATH_2004__339_11_775_0 ER -
Shanjian Tang; Xu Zhang. Carleman inequality for backward stochastic parabolic equations with general coefficients. Comptes Rendus. Mathématique, Volume 339 (2004) no. 11, pp. 775-780. doi : 10.1016/j.crma.2004.09.036. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.09.036/
[1] Carleman estimate and controllability of linear stochastic heat equations, Appl. Math. Optim., Volume 47 (2003), pp. 97-120
[2] On the approximate controllability of a stochastic parabolic equation with a multiplicative noise, C. R. Acad. Sci. Paris, Ser. I, Volume 328 (1999), pp. 675-680
[3] Controllability of Evolution Equations, Lecture Notes Ser., vol. 34, Research Institute of Mathematics, Seoul National University, Seoul, Korea, 1994
[4] S. Tang, X. Zhang, Null controllability for forward and backward stochastic parabolic equations, Preprint
Cited by Sources:
Comments - Policy