Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this article, the exact master equation of Prigogine and Resibois is derived for inhomogeneous as well as homogeneous systems from the following postulate: the singularities of the analytically continued Liouville resolvent nearest the real axis are isolated simple poles arising from irreducible vacuum-to-vacuum transitions.
Abstract: The exact master equation of Prigogine and Resibois is derived for inhomogeneous as well as homogeneous systems. The asymptotic master equation is obtained from the following postulate: The singularities of the analytically continued Liouville resolvent nearest the real axis are isolated simple poles arising from “irreducible vacuum‐to‐vacuum” transitions. The asymptotic distribution function found in this way differs from the one obtained previously. If the asymptotic distribution function at time t1, fa(t1) is taken as a new initial value in the exact master equation, and the subsequent asymptotic solution is calculated for a time t2 later, the result is fa(t1 + t2).
6 citations
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6 citations
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TL;DR: In this article, the asymptotic properties of the nonparametric estimation of K-function in stationary spatial point processes have been studied, and the authors investigated the non-stationary K-functions for a class of nonstationary processes, where stationary is often not a reasonable assumption.
Abstract: The K-function is one of the most commonly used summary statistics. It plays the role for spatial point processes that the covariance function or the variogram plays for continuous observation. The asymptotic properties of the nonparametric estimation of K-function in stationary spatial point processes have been studied. However, in practice, stationary is often not a reasonable assumption. In this article, we investigate the asymptotic behaviour of the nonparametric estimation of K-function for a class of nonstationary processes.
5 citations
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TL;DR: In this paper, a class of second order difference equations with three paremeters is studied and the asymptotic behavior of positive solutions with positive initial values is investigated.
Abstract: In this paper, we study a class of second order difference equations with three paremeters. With positive initial values, the asymptotic behavior of positive solutions are investigated.
5 citations
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TL;DR: In this paper, the authors gave the complete asymptotic expansion of the measure of approximation of the Abel-Poisson integral for functions of the Lipschitz class.
Abstract: We give the complete asymptotic expansion of the measure of approximation of the Abel-Poisson integral for functions of Lipschitz class.
5 citations