Showing papers by "Hitoshi Ishii published in 1985"

A PDE approach to some asymptotic problems concerning random differential equations with small noise intensities

Abstract: We illustrate the effectiveness of viscosity solution methods for Hamilton-Jacobi PDE by demonstrating a new approach to a method of W. Fleming ( [ , [ ) for proving WKB-type representations. We present new proofs of three examples, due originally to Ventcel-Freidlin, Varadhan, and Fleming.

On Representation of Solutions of Hamilton-Jacobi Equations with Convex Hamiltonians

Abstract: Publisher Summary Recently, Crandall and Lions introduced the notion of viscosity solution for Hamilton–Jacobi equations to settle the uniqueness problem of generalized solutions of Hamilton–Jacobi equations. The existence of viscosity solutions of Hamilton–Jacobi equations was established under the same hypotheses on the Hamiltonians as those for the uniqueness of viscosity solutions. Thus, the chapter presents the Hamiltonian as a max or max–min of linear functions of p, and proves the uniform continuity of the value function of the associated optimal control or differential game problem.