Eikonal equations and pathwise solutions to fully non-linear SPDEs

TL;DR

This paper investigates the existence and uniqueness of stochastic viscosity solutions for fully nonlinear second-order SPDEs with quadratic Hamiltonians in a Riemannian setting, extending previous work in the field.

Contribution

It introduces new results on stochastic viscosity solutions for a broader class of fully nonlinear SPDEs with quadratic Hamiltonians, expanding the scope of prior research.

Findings

Established existence and uniqueness of solutions

Extended the class of equations studied to include degenerate cases

Connected solutions to Riemannian geometric frameworks

Abstract

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 Riemannian geometry. The results are new and extend the class of equations studied so far by the last two authors.