Regularity for nonlinear stochastic games
Luiro, H., & Parviainen, M. (2018). Regularity for nonlinear stochastic games. Annales de l'Institut Henri Poincaré : Analyse non linéaire, 35 (6), 1435-1456. doi:10.1016/j.anihpc.2017.11.009
© Elsevier 2018
We establish regularity for functions satisfying a dynamic programming equation, which may arise for example from stochastic games or discretization schemes. Our results can also be utilized in obtaining regularity and existence results for the corresponding partial differential equations.
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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 ...
Arroyo Garcia, Angel; Luiro, Hannes; Parviainen, Mikko; Ruosteenoja, Eero (Springer, 2020)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 ...
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 ...