This book investigates the relationship between controlled Markov processes and viscosity solutions to Hamilton-Jacobi-Bellman equations. It presents a unified approach to the analysis of stochastic differential games and optimal control problems, drawing on recent advances in the theory of viscosity solutions. The authors explore the connection between the value function of a stochastic control problem and the viscosity solution of the associated Hamilton-Jacobi-Bellman equation, providing a rigorous framework for understanding these complex systems.

The book is recognized as a significant contribution to the field of stochastic control and viscosity solutions, offering a rigorous and unified treatment of these topics. Its depth and mathematical sophistication suggest it is primarily aimed at researchers and advanced graduate students in mathematics, engineering, and economics. The work is expected to be a valuable resource for those seeking to understand the theoretical underpinnings of optimal control and differential games in stochastic environments.