Random walks and random tug of war in the Heisenberg group

2018/11/08 by Lewicka, Marta, Manfredi, Juan, Ricciotti, Diego
#35H20 #35J70 #35R03 #91A15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.04765

Abstract

We study the mean value properties of p-harmonic functions on the first Heisenberg group ℍ, in connection to the dynamic programming principles of certain stochastic processes. We implement the approach of Peres-Scheffield to provide the game-theoretical interpretation of the sub-elliptic p-Laplacian; and of Manfredi-Parviainen-Rossi to characterize its viscosity solutions via the asymptotic mean value expansions.

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