Topic
Rate of convergence
About: Rate of convergence is a research topic. Over the lifetime, 31257 publications have been published within this topic receiving 795334 citations. The topic is also known as: convergence rate.
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TL;DR: It is shown that the algorithm converges to the characteristic as the number of observations tend to infinity, for sufficiently smooth characteristics, the rate of convergence is O(n^{-2/5}) in probability.
Abstract: In this note a discrete-time Hammerstein system is identified. The weighting function of the dynamical subsystem is recovered by the correlation method. The main results concern estimation of the nonlinear memoryless subsystem. No conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented.The algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data. It is shown that the algorithm converges to the characteristic as the number of observations tend to infinity. For sufficiently smooth characteristics, the rate of convergence is O(n^{-2/5}) in probability.
171 citations
TL;DR: In this article, the authors show that the rate of convergence depends on the smoothness of option payoff functions, and is much lower than commonly believed because option payoff function are often of all-or-nothing type and are not continuously differentiable.
Abstract: This paper characterizes the rate of convergence of discrete-time multinomial option prices. We show that the rate of convergence depends on the smoothness of option payoff functions, and is much lower than commonly believed because option payoff functions are often of all-or-nothing type and are not continuously differentiable. To improve the accuracy, we propose two simple methods, an adjustment of the discrete-time solution prior to maturity and smoothing of the payoff function, which yield solutions that converge to their continuous-time limit at the maximum possible rate enjoyed by smooth payoff functions. We also propose an intuitive approach that systematically derives multinomial models by matching the moments of a normal distribution. A highly accurate trinomial model also is provided for interest rate derivatives. Numerical examples are carried out to show that the proposed methods yield fast and accurate results.
171 citations
TL;DR: Under certain conditions, it is proved that the Cohen-Grossberg neural networks system is exponentially stable globally or convergent globally in finite time.
171 citations
TL;DR: It is found that in general, the possibility of coordination is more likely to arise when the overall level of noise is low and when the public information is relatively informative, and higher-order uncertainty vanishes, as the noise in the signals disappears.
171 citations
TL;DR: The nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations are obtained by introducing a new notion of consistency.
Abstract: . We obtain nonsymmetric upper and lower bounds on the rate of convergence of general monotone approximation/numerical schemes for parabolic Hamilton-Jacobi-Bellman equations by introducing a new notion of consistency. Our results are robust and general - they improve and extend earlier results by Krylov, Barles, and Jakobsen. We apply our general results to various schemes including Crank-Nicholson type finite difference schemes, splitting methods, and the classical approximation by piecewise constant controls. In the first two cases our results are new, and in the last two cases the results are obtained by a new method which we develop here.
171 citations