Eikonal equations and pathwise solutions to fully non-linear SPDEs

Peter K Friz (1, 2) , Paul Gassiat (3) , Pierre Louis Lions (3, 4) , Panagiotis E Souganidis (5)

1 TU - Technical University of Berlin / Technische Universität Berlin
2 WIAS - Weierstraß-Institut für Angewandte Analysis und Stochastik = Weierstrass Institute for Applied Analysis and Stochastics [Berlin]
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
4 Collège de France - Chaire Équations aux dérivées partielles et applications
5 Department of Mathematics [Chicago]

We study the existence and uniqueness of the stochastic viscosity solutions of fully nonlinear, possibly degenerate, second order stochastic pde with quadratic Hamiltonians associated to a Rie-mannian geometry. The results are new and extend the class of equations studied so far by the last two authors.

Mots clés: Fully non-linear stochastic partial differential equations; eikonal equations; pathwise; stability; rough paths; 60H15

Domaines: Probabilités [math.PR]

Peter K Friz, Paul Gassiat, Pierre Louis Lions, Panagiotis E Souganidis. Eikonal equations and pathwise solutions to fully non-linear SPDEs. Stochastics and Partial Differential Equations: Analysis and Computations, 2016, ⟨10.1007/s40072-016-0087-9⟩. ⟨hal-01419770⟩