Iteration convergence speed estimation using the LIL

On the Speed of Convergence of Iteration of a Function

Let fn(X) be the nth iterate of a function in some interval [0, c]. It is known that if f(x) xxc, a > 1, then fn(X) An for some A and a. In this paper we prove a converse of this theorem: The rate of convergence of the iterates determines the form of a function.

On the moment convergence rates of LIL in Hilbert space

Let {X, Xn; n ≥ 1} be a sequence of i.i.d. random variables taking values in a real separable Hilbert space (H, ‖ · ‖) with mean zero and covariance Σ and set Sn = ∑n k=1 Xk , n ≥ 1. Let σ 2 i , i ≥ 1 be the eigenvalues of Σ arranged in non-increasing order and take into account the multiplicities. Let l be the dimension of the corresponding eigenspace of largest eigenvalue σ 2 = σ 2 1 . Let lo...

Asymptotics for the Moment Convergence of U-Statistics in LIL

Convergence Properties of Policy Iteration

This paper analyzes asymptotic convergence properties of policy iteration in a class of stationary, infinite-horizon Markovian decision problems that arise in optimal growth theory. These problems have continuous state and control variables and must therefore be discretized in order to compute an approximate solution. The discretization may render inapplicable known convergence results for poli...

Convergence Analysis of Policy Iteration

Adaptive optimal control of nonlinear dynamic systems with deterministic and known dynamics under a known undiscounted infinite-horizon cost function is investigated. Policy iteration scheme initiated using a stabilizing initial control is analyzed in solving the problem. The convergence of the iterations and the optimality of the limit functions, which follows from the established uniqueness o...