Comparison Principle for Hamilton-Jacobi-Bellman Equations via a Bootstrapping Procedure

Abstract We study the well-posedness of Hamilton–Jacobi–Bellman equations on subsets $${\mathbb {R}}^d$$ R d in a context without boundary conditions. The Hamiltonian is given as supremum over two parts: an internal depending external control variable and cost functional penalizing control. key feature this paper that function can be unbounded discontinuous. This way we treat functionals appear e.g. Donsker–Varadhan theory large deviations for occupation-time measures. To allow flexibility, assume have controlled growth, they satisfy equi-continuity estimate uniformly compact sets space controls. In addition to establishing comparison principle equation, also prove existence, viscosity solution being value with exponentially discounted running costs. As application, verify conditions examples.