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.

In this paper, we will present a modification of the preconditioned AOR-type method for solving the linear system. A theorem is given to show the convergence rate of modification of the preconditioned AOR methods that can be enlarged than the convergence AOR method.

after establishment of the world trade organization (wto) in 1995, not only all countries around the world had to receive progressively the wto accession but also those that had higher economic potentials benefited further advantages from their memberships. one goal which has been followed by the wto has relied on economic convergence. it is now a time to ask whether convergence in monetary po...

The probabilistic properties of eigenvalues of random matrices whose dimension increases indefinitely has received considerable attention. One important aspect is the existence and identification of the limiting spectral distribution (LSD) of the empirical distribution of the eigenvalues. When the LSD exists, it is useful to know the rate at which the convergence holds. The main method to estab...

We extend the approach of Walker (2003, 2004) to the case of misspecified models. A sufficient condition for establishing rates of convergence is given based on a key identity involving martingales, which does not require construction of tests. We also show roughly that the result obtained by using tests can also be obtained by our approach, which demonstrates the potential wider applicability ...

In a simple, forward looking linear stochastic model we investigate the impact of heterogeneity in expectations formation on the speed of convergence of the learning process of agents towards equilibrium. We …nd that even when heterogeneity does not a¤ect learnability in term of its asymptotic outcome, it can still have an important impact on the learnability of an equilibrium in terms of the s...

Let the martingale Wn = Zn mn , where Zn is a weighted branching process and m = E ∑ i Ti is the expected sum of the = factors Ti, converge to some limiting random variable W . We give conditions in terms of the factors such that W belongs to the domain of attraction or to the domain of normal attraction of an = α–stable distribution with 1 < α ≤ 2. Further the rate of convergence of Wn to W is...

We give a strong approximation of Rosenblatt process via transport processes and we give the rate of convergence.

This paper contains an asymptotic analysis of a fluid model for a heavily loaded processor sharing queue. Specifically, we consider the behavior of solutions of critical fluid models as time approaches ∞. The main theorems of the paper provide sufficient conditions for a fluid model solution to converge to an invariant state and, under slightly more restrictive assumptions, provide a rate of co...

We prove sharp convergence rates for a class of domain embedding methods for elliptic boundary value problems. The theory is established for Dirichlet, Neumann, and Robin boundary conditions, and is unified in a new formulation for mixed boundary condition. On the continuous level, the methods for these boundary value problems perform equally well.