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February 2018 Uniform measure density condition and game regularity for tug-of-war games
Joonas Heino
Bernoulli 24(1): 408-432 (February 2018). DOI: 10.3150/16-BEJ882


We show that a uniform measure density condition implies game regularity for all $2<p<\infty$ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for the associated stopping times and density estimates for the sum of independent and identically distributed random vectors.


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Joonas Heino. "Uniform measure density condition and game regularity for tug-of-war games." Bernoulli 24 (1) 408 - 432, February 2018.


Received: 1 October 2015; Revised: 1 March 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778334
MathSciNet: MR3706763
Digital Object Identifier: 10.3150/16-BEJ882

Keywords: $p$-harmonic functions , $p$-regularity , density estimate for the sum of i.i.d. random vectors , game regularity , hitting probability , Stochastic games , uniform distribution in a ball , uniform measure density condition

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 1 • February 2018
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