Tug-of-war with Kolmogorov

We introduce a new class of strongly degenerate nonlinear parabolic PDEs ( p − 2 ) Δ ∞ , X N + u Y t m ⋅ ∇ ∂ = 0 ∈ R × 1 combining the classical PDE Kolmogorov and normalized -Laplace operator. characterize solutions in terms an asymptotic mean value property results are connected to analysis certain tug-of-war games with noise. The functions for introduced approximate stated when parameter that controls size possible steps goes zero. Existence uniqueness viscosity Dirichlet problem is established. property, associated geometry underlying problem, all reflect family dilation Lie group operators type, this makes our setting different from context standard dilations Euclidean translations applicable heat operator infinity Laplace