The functional autoregressive model is a Markov model taylored for data of functional nature. It revealed fruitful when attempting to model samples of dependent random curves and has been widely studied along the past few years. This article aims at completing the theoretical study of the model by adressing the crucial issue of weak convergence for estimates from the model. The main difficultie...

This compact set of notes present some basic, abstract results with two examples of boundary-value problems on weak convergence methods for the study of existence of minimizers of essentially convex functionals. The method described here is called the direct method in the calculus of variations. The main results are stated in their simplest possible setting. But, they have many variations that ...

1. Introduction. We will show that if a sequence of domains D k increases to a domain D then the reflected Brownian motions in D k 's converge to the reflected Brownian motion in D, under mild technical assumptions. Our theorem follows easily from known results and is perhaps known as a " folk law " among the specialists but it does not seem to be recorded anywhere in an explicit form. The purp...

Author’s note. The authors were visiting Dalhousie University in 1988 during a seventeen-day labor dispute that left the Mathematics Department empty. During this period they occupied themselves writing the present paper, on a natural topic in variational analysis known elsewhere as “scalar convergence” [22, 16, 4, 17, 3, 18]. Although referenced in the literature [19, 2], this work was never p...

In this paper we introduce and study a weakened form of logarithmic Sobolev inequalities in connection with various others functional inequalities (weak Poincaré inequalities, general Beckner inequalities...). We also discuss the quantitative behaviour of relative entropy along a symmetric diffusion semi-group. In particular, we exhibit an example where Poincaré inequality can not be used for d...

In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.

The aim of this paper is to investigate the weak convergence for negatively associated random #elds. To this end, we obtain some moment inequalities for the maximum of partial sums for a negatively associated random #eld, which also are of independent interest. c © 2001 Elsevier Science B.V. All rights reserved MSC: primary 60F05; secondary 62E20

We present a random probability distribution which approximates, in the sense of weak convergence, the Dirichlet process and supports a Bayesian resampling plan called a proper Bayesian bootstrap. 2000 Mathematics Subject Classification: 62G09, 60B10.

Conditions suitable for applications in finance are given for the weak convergence (or convergence in probability) of stochastic integrals. For example, consider a sequence Sn of security price processes converging in distribution to S and a sequence 8" of trading strategies converging in distribution to 0. We survey conditions under which the financial gain process J 0" dSn converges in distri...

The asymptotic validity of tests is usually established by making appropriate primitive assumptions, which imply the weak convergence of a specific function of the data, and an appeal to the continuous mapping theorem. This paper, instead, takes the weak convergence of some function of the data to a limiting random element as the starting point, and studies efficiency in the class of tests that...