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
••
TL;DR: In this article, the asymptotic solution for the displacement distribution in the Reissner plate becomes infinite for some special vertex angles of the notch, this is a paradox and the corresponding bounded solutions are explained by the Jordan form solution according to the methods of mathematical physics.
3 citations
••
3 citations
••
TL;DR: In this article, the nonlinear theory of viscoelasticity is described by nonlinear integrodifferential and integral equations and asymptotic expansions of the solutions of these equations are given.
Abstract: Dynamic and quasistatic problems of the nonlinear theory of viscoelasticity are described by nonlinear integrodifferential and integral equations. Methods of averaging various classes of nonlinear integrodifferential and integral equations are described and asymptotic expansions of the solutions of these equations are given.
3 citations
••
TL;DR: In this paper, a multi-scale method was used to construct an asymptotic solution of the auto-resonance arising problem in the domain t ≪ e −1.
Abstract: The problem of auto-resonance arising is investigated. Using the multi-scale method, we construct an asymptotic solution of this problem in the domain t ≪ e
−1
3 citations
••
01 Jan 2000TL;DR: This chapter is devoted to providing a modern asymptotic estimation and testing theory for those various stochastic process models, such as, nonlinear time series models, diffusion processes, point processes, and nonergodic processes.
Abstract: In classical time series analysis the asymptotic estimation and testing theory was developed for linear processes, which include the AR, MA, and ARMA models. However, in the last twenty years a lot of more complicated stochastic process models have been introduced, such as, nonlinear time series models, diffusion processes, point processes, and nonergodic processes. This chapter is devoted to providing a modern asymptotic estimation and testing theory for those various stochastic process models. The approach is mainly based on the LAN results given in the previous chapter. More concretely, in Section 3.1 we discuss the asymptotic estimation and testing theory for non-Gaussian vector linear processes in view of LAN. The results are very general and grasp a lot of other works dealing with AR, MA, and ARMA models as special cases. Section 3.2 reviews some elements of nonlinear time series models and the asymptotic estimation theory based on the conditional least squares estimator and maximum likelihood estimator (MLE). We address the problem of statistical model selection in general fashion. Also the asymptotic theory for nonergodic models is mentioned. Recently much attention has been paid to continuous time processes (especially diffusion processes), which appear in finance. Hence, in Section 3.3 we describe the foundation of stochastic integrals and diffusion processes. Then the LAN-based asymptotic theory of estimation for them is studied.
3 citations