Voir la notice de l'article provenant de la source Numdam
We consider non-linear parabolic evolution equations of the form , subject to noise of the form where H is linear in Du and denotes the Stratonovich differential of a multi-dimensional Brownian motion. Motivated by the essentially pathwise results of [P.-L. Lions, P.E. Souganidis, Fully nonlinear stochastic partial differential equations, C. R. Acad. Sci. Paris Sér. I Math. 326 (9) (1998) 1085–1092] we propose the use of rough path analysis [T.J. Lyons, Differential equations driven by rough signals, Rev. Mat. Iberoamericana 14 (2) (1998) 215–310] in this context. Although the core arguments are entirely deterministic, a continuity theorem allows for various probabilistic applications (limit theorems, support, large deviations, …).
@article{AIHPC_2011__28_1_27_0,
author = {Caruana, Michael and Friz, Peter K. and Oberhauser, Harald},
title = {A (rough) pathwise approach to a class of non-linear stochastic partial differential equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {27--46},
publisher = {Elsevier},
volume = {28},
number = {1},
year = {2011},
doi = {10.1016/j.anihpc.2010.11.002},
mrnumber = {2765508},
zbl = {1219.60061},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2010.11.002/}
}
TY - JOUR AU - Caruana, Michael AU - Friz, Peter K. AU - Oberhauser, Harald TI - A (rough) pathwise approach to a class of non-linear stochastic partial differential equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 27 EP - 46 VL - 28 IS - 1 PB - Elsevier UR - http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2010.11.002/ DO - 10.1016/j.anihpc.2010.11.002 LA - en ID - AIHPC_2011__28_1_27_0 ER -
%0 Journal Article %A Caruana, Michael %A Friz, Peter K. %A Oberhauser, Harald %T A (rough) pathwise approach to a class of non-linear stochastic partial differential equations %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 27-46 %V 28 %N 1 %I Elsevier %U http://geodesic.mathdoc.fr/articles/10.1016/j.anihpc.2010.11.002/ %R 10.1016/j.anihpc.2010.11.002 %G en %F AIHPC_2011__28_1_27_0
Caruana, Michael; Friz, Peter K.; Oberhauser, Harald. A (rough) pathwise approach to a class of non-linear stochastic partial differential equations. Annales de l'I.H.P. Analyse non linéaire, Tome 28 (2011) no. 1, pp. 27-46. doi: 10.1016/j.anihpc.2010.11.002
Cité par Sources :