DYNAMIC PROGRAMMING, SUCCESSIVE APPROXIMATIONS, AND MONOTONE CONVERGENCE

Monotone Dynamic Programming

By integrating dynamic programming with the theory of order preserving dynamical systems (Hirsch (1982), Smith (1995)) this paper develops a new approach to stability analysis in continuous-time dynamic optimization models. The main results provide simple conditions on the primitives of a model which imply that steady states exist and are globally stable for initial conditions in an open dense ...

Functional Approximations and Dynamic Programming

Improving Convergence Rate in the Method of Successive Approximations*

An application of the method of successive approximations for obtaining the solution of a nonlinear integral equation arising from a two-point boundary value problem is illustrated. In particular, we show sufficient conditions under which the convergence rate of the sequence can be improved.

Monotone Dynamic Programming: Director’s Cut

By integrating dynamic programming with the theory of order preserving dynamical systems (Hirsch (1982), Smith (1995)) this paper develops a new approach to stability analysis in dynamic economic models. The main results provide simple conditions on the primitives of a model which imply that steady states are globally stable for almost all initial conditions. If the steady state is unique or la...

Convergence of the natural approximations of piecewise monotone interval maps.

We consider piecewise monotone interval mappings which are topologically mixing and satisfy the Markov property. It has previously been shown that the invariant densities of the natural approximations converge exponentially fast in uniform pointwise topology to the invariant density of the given map provided its derivative is piecewise Lipshitz continuous. We provide an example of a map which i...