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Stochastic differential games with competing Brownian particles and related Isaacs' equations
Author(s) -
Feng Xinwei
Publication year - 2017
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2356
Subject(s) - brownian motion , stochastic differential equation , mathematics , viscosity solution , nonlinear system , stochastic partial differential equation , mathematical analysis , differential equation , physics , statistics , quantum mechanics
Summary In this paper, we study zero‐sum two‐player stochastic differential games in which the state equations are competing Brownian particles and the cost functional is defined by generalized backward stochastic differential equations with more than one increasing process. After we study the regularity of competing Brownian particles, we establish the dynamic programming principle for the upper and lower value functions and show that these are the unique viscosity solution of the associated upper and lower Isaacs' equations, which are fully nonlinear parabolic partial differential equations with nonlinear Neumann boundary conditions.