Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities
Arroyo Garcia, A., Luiro, H., Parviainen, M., & Ruosteenoja, E. (2020). Asymptotic Lipschitz regularity for tug-of-war games with varying probabilities. Potential Analysis, 53(2), 565–589. https://doi.org/10.1007/s11118-019-09778-8
Published inPotential Analysis
© 2019 the Authors
We prove an asymptotic Lipschitz estimate for value functions of tug-of-war games with varying probabilities defined in Ω ⊂ ℝn. The method of the proof is based on a game-theoretic idea to estimate the value of a related game defined in Ω ×Ω via couplings.
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Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingOpen access funding provided by University of Jyväskylä (JYU). The authors have been supported by the Academy of Finland project #298641. Á. A. was partially supported by the grant MTM2017-85666-P.
Showing items with similar title or keywords.
Ruosteenoja, Eero (University of Jyväskylä, 2017)
Attouchi, Amal; Luiro, Hannes; Parviainen, Mikko (Society for Industrial and Applied Mathematics, 2021)We define a random step size tug-of-war game and show that the gradient of a value function exists almost everywhere. We also prove that the gradients of value functions are uniformly bounded and converge weakly to the ...
Heino, Joonas (International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability, 2018)We show that a uniform measure density condition implies game regularity for all 2 < p < ∞ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for ...
Heino, Joonas (University of Jyväskylä, 2018)This thesis studies local and global regularity properties of a stochastic two-player zero-sum game called tug-of-war. In particular, we study value functions of the game locally as well as globally, that is, close to ...
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