On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains and the Isaacs equations

DOI10.1007/s00440-013-0495-yzbMath1290.91022arXiv1205.0050OpenAlexW2066572496MaRDI QIDQ2447298

Nicolai V. Krylov

Publication date: 25 April 2014

Published in: Probability Theory and Related Fields (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.0050

zbMATH Keywords

stochastic gamesdynamic programming principleIsaacs equations

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Differential games and control (49N70) Differential games (aspects of game theory) (91A23) Dynamic programming (90C39) Stochastic games, stochastic differential games (91A15) PDEs in connection with game theory, economics, social and behavioral sciences (35Q91)

Related Items (10)

On the Rate of Convergence of Finite-Difference Approximations for Elliptic Isaacs Equations in Smooth Domains ⋮ Zero-sum path-dependent stochastic differential games in weak formulation ⋮ GANs training: A game and stochastic control approach ⋮ A Probabilistic Representation for the Value of Zero-Sum Differential Games with Incomplete Information on Both Sides ⋮ On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains ⋮ On regularity properties and approximations of value functions for stochastic differential games in domains ⋮ Approximating the value functions for stochastic differential games with the ones having bounded second derivatives ⋮ On the second order derivatives of solutions of a special Isaacs equation ⋮ A neural network-based policy iteration algorithm with global \(H^2\)-superlinear convergence for stochastic games on domains ⋮ On the independence of the value function for stochastic differential games of the probability space

Cites Work

• On the existence of smooth solutions for fully nonlinear elliptic equations with measurable ``coefficients without convexity assumptions
• On regularity properties and approximations of value functions for stochastic differential games in domains
• Another approach to the existence of value functions of stochastic differential games
• Elliptic partial differential equations of second order
• On the dynamic programming principle for uniformly nondegenerate stochastic differential games in domains
• Stochastic Differential Games and Viscosity Solutions of Hamilton–Jacobi–Bellman–Isaacs Equations
• Stochastic differential games and viscosity solutions of Isaacs equations
• Value functions and the Dirichlet problem for Isaacs equation in a smooth domain
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