A STOCHASTIC DIFFERENTIAL GAME FOR THE INHOMOGENEOUS ∞-LAPLACE EQUATION

被引：15

作者：

Atar, Rami ^{[1
]}

Budhiraja, Amarjit ^{[2
]}

机构：

[1] Technion Israel Inst Technol, Dept Elect Engn, IL-32000 Haifa, Israel

[2] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27599 USA

来源：

ANNALS OF PROBABILITY | 2010年 / 38卷 / 02期

关键词：

Stochastic differential games; infinity-Laplacian; Bellman-Isaacs equation; EXISTENCE; CURVATURE;

D O I：

10.1214/09-AOP494

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：

Given a bounded C(2) domain G subset of R(m), functions g is an element of C(partial derivative G, R) and h is an element of C((G) over bar, R backslash {0}), let u denote the unique viscosity solution to the equation -2 Delta(infinity)u = h in G with boundary data g. We provide a representation for u as the value of a two-player zero-sum stochastic differential game.

引用

页码：498 / 531

页数：34

共 50 条

[11] Intermittency and stochastic pseudo-differential equation with spatially inhomogeneous white noise
Junfeng Liu
Nonlinear Differential Equations and Applications NoDEA, 2019, 26
[12] A STOCHASTIC EQUATION FOR DISPERSION IN INHOMOGENEOUS CONDITIONS
DEBAAS, AF
TROEN, I
PHYSICA SCRIPTA, 1989, 40 (01): : 64 - 72
[13] A kind of non-zero sum mixed differential game of backward stochastic differential equation
Zhang, Huanjun
ADVANCES IN DIFFERENCE EQUATIONS, 2020, 2020 (01)
[14] A kind of non-zero sum mixed differential game of backward stochastic differential equation
Huanjun Zhang
Advances in Difference Equations, 2020
[15] The stochastic p-Laplace equation on Rd
Schmitz, Kerstin
Zimmermann, Aleksandra
STOCHASTIC ANALYSIS AND APPLICATIONS, 2023, 41 (05) : 892 - 917
[16] STOCHASTIC DIFFERENTIAL EQUATION
CAIROLI, R
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1972, 274 (24): : 1739 - &
[17] On a differential game in a stochastic system
Vlasenko, L. A.
Rutkas, A. G.
Chikrii, A. A.
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2019, 25 (03): : 45 - 61
[18] On a Differential Game in a Stochastic System
Vlasenko, L. A.
Rutkas, A. G.
Chikrii, A. A.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2020, 309 (SUPPL 1) : S185 - S198
[19] A STOCHASTIC DIFFERENTIAL REINSURANCE GAME
Zeng, Xudong
JOURNAL OF APPLIED PROBABILITY, 2010, 47 (02) : 335 - 349
[20] A Stochastic differential game in the orthrant
Ghosh, MK
Kumar, KS
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 265 (01) : 12 - 37

← 1 2 3 4 5 →