Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
Papers published on a yearly basis
Papers
More filters
••
289 citations
••
286 citations
••
TL;DR: In this article, the asymptotic behavior of solutions for parabolic non-linear evolution equations in R n is studied and the existence of the global attractor in L 2 (R n ) is established.
272 citations
••
TL;DR: In this paper, the authors consider the case where the population value of the parameter vector is a boundary point of the feasible region and show that the asymptotic distribution of test statistic is a mixture of chi-squared distributions.
Abstract: SUMMARY The analysis of moment structural models has become an important tool of investigation in behavioural, educational and economic studies. The chi-squared largesample test is routinely employed to assess the goodness of fit of the model considered. However, in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met. Here we consider the case where the population value of the parameter vector is a boundary point of the feasible region. We show that in this case the asymptotic distribution of test statistic is a mixture of chi-squared distributions. The problem of finding the corresponding weights is discussed.
269 citations
••
TL;DR: In this article, the authors use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a hyperasymptotic approximation.
Abstract: Singular perturbation methods, such as the method of multiple scales and the method of matched asymptotic expansions, give series in a small parameter e which are asymptotic but (usually) divergent. In this survey, we use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a 'hyperasymptotic' approximation. This adds a second asymptotic expansion, with different scaling assumptions about the size of various terms in the problem, to achieve a minimum error much smaller than the best possible with the original asymptotic series. (This rescale-and-add process can be repeated further.) Weakly nonlocal solitary waves are used as an illustration.
261 citations