We prove the existence and uniqueness of solutions to a class of stochastic scalar conservation laws with joint space–time transport noise and affine-linear noise driven by a geometric p-rough path. In particular, stability of the solutions with respect to the driving rough path is obtained, leading to a robust approach to stochastic scalar conservation laws. As immediate corollaries we obtain support theorems, large deviation results and the generation of a random dynamical system.
Mots clés : Stochastic scalar conservation laws, Rough paths, Random dynamical systems, Stability, Kružkov entropy solutions
@article{AIHPC_2016__33_4_933_0,
author = {Friz, Peter K. and Gess, Benjamin},
title = {Stochastic scalar conservation laws driven by rough paths},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {933--963},
publisher = {Elsevier},
volume = {33},
number = {4},
year = {2016},
doi = {10.1016/j.anihpc.2015.01.009},
mrnumber = {3519527},
zbl = {1345.60055},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.01.009/}
}
TY - JOUR AU - Friz, Peter K. AU - Gess, Benjamin TI - Stochastic scalar conservation laws driven by rough paths JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 933 EP - 963 VL - 33 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.01.009/ DO - 10.1016/j.anihpc.2015.01.009 LA - en ID - AIHPC_2016__33_4_933_0 ER -
%0 Journal Article %A Friz, Peter K. %A Gess, Benjamin %T Stochastic scalar conservation laws driven by rough paths %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 933-963 %V 33 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.01.009/ %R 10.1016/j.anihpc.2015.01.009 %G en %F AIHPC_2016__33_4_933_0
Friz, Peter K.; Gess, Benjamin. Stochastic scalar conservation laws driven by rough paths. Annales de l'I.H.P. Analyse non linéaire, Tome 33 (2016) no. 4, pp. 933-963. doi : 10.1016/j.anihpc.2015.01.009. http://www.numdam.org/articles/10.1016/j.anihpc.2015.01.009/
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