Random walks and random tug of war in the Heisenberg group

Marta Lewicka; Juan Manfredi; Diego Ricciotti

Random walks and random tug of war in the Heisenberg group

Analysis of PDEs 2019-05-01 v2

Authors: Marta Lewicka , Juan Manfredi , Diego Ricciotti

Abstract

We study the mean value properties of $\mathbf{p}$ -harmonic functions on the first Heisenberg group $\mathbb{H}$ , 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 $\mathbf{p}$ -Laplacian; and of Manfredi-Parviainen-Rossi to characterize its viscosity solutions via the asymptotic mean value expansions.

Keywords

heisenberg group p-harmonic functions random walk tug of war sub-elliptic p-laplacian viscosity solutions

Cite

@article{arxiv.1811.04765,
  title  = {Random walks and random tug of war in the Heisenberg group},
  author = {Marta Lewicka and Juan Manfredi and Diego Ricciotti},
  journal= {arXiv preprint arXiv:1811.04765},
  year   = {2019}
}

Comments

39 pages, 4 figures. arXiv admin note: text overlap with arXiv:1810.03413

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