2023/04/21 by Félix del Teso, Jørgen Endal, Espen R. Jakobsen +1
Economics, Econometrics and Finance · Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Stochastic processes and financial applications
paper · pdf · doi:10.1007/s00526-023-02475-w
openalex publication_date 2023/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Abstract We consider the evolution problem associated to the infinity fractional Laplacian introduced by Bjorland et al. (Adv Math 230(4–6):1859–1894, 2012) as the infinitesimal generator of a non-Brownian tug-of-war game. We first construct a class of viscosity solutions of the initial-value problem for bounded and uniformly continuous data. An important result is the equivalence of the nonlinear operator in higher dimensions with the one-dimensional fractional Laplacian when it is applied to radially symmetric and monotone functions. Thanks to this and a comparison theorem between classical and viscosity solutions, we are able to establish a global Harnack inequality that, in particular, explains the long-time behavior of the solutions.