2020/04/05 by Zhou, Jianjun
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2004.02095
In this article, a notion of viscosity solutions is introduced for first order path-dependent Hamilton-Jacobi-Bellman (HJB) equations associated with optimal control problems for path-dependent differential equations. We identify the value functional of the optimal control problems as a unique viscosity solution to the associated HJB equations. We also show that our notion of viscosity solutions is consistent with the corresponding notion of classical solutions, and satisfies a stability property.