A game theoretical approximation for a parabolic/elliptic system with different operators
Analysis of PDEs
2021-06-29 v1 Probability
Abstract
In this paper we find viscosity solutions to a coupled system composed by two equations, the first one is parabolic and driven by the infinity Laplacian while the second one is elliptic and involves the usual Laplacian. We prove that there is a two-player zero-sum game played in two different boards with different rules in each board (in the first one we play a Tug-of-War game taking the number of plays into consideration and in the second board we move at random) whose value functions converge uniformly to a viscosity solution to the PDE system.
Keywords
Cite
@article{arxiv.2106.14088,
title = {A game theoretical approximation for a parabolic/elliptic system with different operators},
author = {Alfredo Miranda and Julio D. Rossi},
journal= {arXiv preprint arXiv:2106.14088},
year = {2021}
}
Comments
arXiv admin note: substantial text overlap with arXiv:2003.08969