Gradient walks and 𝑝-harmonic functions

Luiro, Hannes; Parviainen, Mikko

doi:10.1090/proc/13540

Gradient walks and $p$-harmonic functions
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by Hannes Luiro and Mikko Parviainen PDF

Proc. Amer. Math. Soc. 145 (2017), 4313-4324 Request permission

Abstract:

We consider a class of stochastic processes having a connection to $p$-harmonic functions. In particular, we obtain stochastic approximations that converge uniformly to a $p$-harmonic function, and also with an explicit convergence rate. The main difficulty is how to deal with the zero set of the gradient of the underlying function.

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