Gradient walks and p-harmonic functions

Gradient walks and p-harmonic functions

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 gradie...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2017-10, Vol.145 (10), p.4313-4324
Hauptverfasser: Luiro, Hannes, Parviainen, Mikko
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13540