Normed Bellman Equation with Degenerate Diffusion Coefficients and Its Application to Differential Equations

摘要

The purpose of this paper is to prove the existence and uniqueness of generalized solution of the normed bellman equation with degenerate diffusion coefficients and also to prove that this unique solution is the cost function of a stochastic control problem associated with the normed Bellman equation. We can apply these results to some interesting degenerate and nonlinear differential equations.