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://archive.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://archive.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://archive.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://archive.numdam.org/articles/10.1016/j.anihpc.2015.01.009/
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