Uniform measure density condition and game regularity for tug-of-war games

被引：1

作者：

Heino, Joonas ^{[1
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35, FI-40014 Jyvaskyla, Finland

来源：

BERNOULLI | 2018年 / 24卷 / 01期

关键词：

density estimate for the sum of i.i.d. random vectors; game regularity; hitting probability; p-harmonic functions; p-regularity; stochastic games; uniform distribution in a ball; uniform measure density condition; P-HARMONIOUS FUNCTIONS; INFINITY LAPLACIAN; BESSEL-FUNCTIONS; EQUATION; ZEROS;

D O I：

10.3150/16-BEJ882

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We show that a uniform measure density condition implies game regularity for all 2 < p < infinity 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.

引用

页码：408 / 432

页数：25

共 36 条

[1] Asymptotic Lipschitz Regularity for Tug-of-War Games with Varying Probabilities
Ángel Arroyo
Hannes Luiro
Mikko Parviainen
Eero Ruosteenoja
[J]. Potential Analysis, 2020, 53 : 565 - 589
[2] Asymptotic Lipschitz Regularity for Tug-of-War Games with Varying Probabilities
Arroyo, Angel
Luiro, Hannes
Parviainen, Mikko
Ruosteenoja, Eero
[J]. POTENTIAL ANALYSIS, 2020, 53 (02) : 565 - 589
[3] Tug-of-war games and PDEs
Rossi, Julio D.
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2011, 141 : 319 - 369
[4] AN OBSTACLE PROBLEM FOR TUG-OF-WAR GAMES
Manfredi, Juan J.
Rossi, Julio D.
Somersille, Stephanie J.
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2015, 14 (01) : 217 - 228
[5] Local regularity for time-dependent tug-of-war games with varying probabilities
Parviainen, Mikko
Ruosteenoja, Eero
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (02) : 1357 - 1398
[6] Introduction to Random Tug-of-War Games and PDEs
Manfredi, Juan J.
[J]. REGULARITY ESTIMATES FOR NONLINEAR ELLIPTIC AND PARABOLIC PROBLEMS: CETRARO, ITALY 2009, 2012, 2045 : 133 - 151
[7] MAGIC RAMIE ROPE FOR THE TUG-OF-WAR GAME
Liu, Guo-Liang
Zhao, Hong-Zhi
Liu, Fu-Juan
LI, Xiao-Xia
Hao, Xi -Bo
[J]. THERMAL SCIENCE, 2023, 27 (3A): : 2127 - 2133
[8] TUG-OF-WAR GAMES AND THE INFINITY LAPLACIAN WITH SPATIAL DEPENDENCE
Gomez, Ivana
Rossi, Julio D.
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2013, 12 (05) : 1959 - 1983
[9] GRADIENT AND LIPSCHITZ ESTIMATES FOR TUG-OF-WAR TYPE GAMES
Attouchi, Amal
Luiro, Hannes
Parviainen, Mikko
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2021, 53 (02) : 1295 - 1319
[10] DYNAMIC PROGRAMMING PRINCIPLE FOR TUG-OF-WAR GAMES WITH NOISE
Manfredi, Juan J.
Parviainen, Mikko
Rossi, Julio D.
[J]. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2012, 18 (01) : 81 - 90

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