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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 paper, for an unknown parameter in the drift function of a diffusion process, an M-estimator based on continuously observed data, and obtain its distributional asymptotic expansion up to the third order.
Abstract: For an unknown parameter in the drift function of a diffusion process, we consider an M-estimator based on continuously observed data, and obtain its distributional asymptotic expansion up to the third order. Our setting covers the misspecified cases. To represent the coefficients in the asymptotic expansion, we derive some formulas for asymptotic cumulants of stochastic integrals, which are widely applicable to many other problems. Furthermore, asymptotic properties of cumulants of mixing processes will be also studied in a general setting.

14 citations

Journal ArticleDOI
TL;DR: Asymptotic expansions for the solution to hyperbolic systems with different time scales in one space dimension were derived in this paper for the general case with singular coefficients at the boundary.
Abstract: Asymptotic expansions are derived for the solution to hyperbolic systems with different time scales in one space dimension. The derivation is made for the general case with singular coefficients at the boundary.

14 citations

Journal ArticleDOI
TL;DR: The Matched Asymptotic Expansion Method (MAPMEM) as discussed by the authors is one of the most well-known methods for fitting line integrals with singular kernels, but it is not well adapted to deal with Finite Part integrals.
Abstract: Asymptotic theories like the lifting-line, the slender body or the slender ship lead to lineintegrals with singular kernels. Sometimes these integrals are “improper”, that is to say that they are defined only by their Finite Part. To find asymptotic expansions of these integrals, the Matched Asymptotic Expansion Method is widely used along with other more specific methods depending on the kernel type. The first method is laborious and not systematic, and the other methods are sometimes too much specific to treat general cases. Moreover, all of them are not well adapted to deal with Finite Part integrals.

14 citations

Journal ArticleDOI
TL;DR: In this article, an asymptotic analysis of the Boltzmann equations (Riccati differential equations) that describe the physics of thermal dark-matter-relic abundances is presented.
Abstract: This paper presents an asymptotic analysis of the Boltzmann equations (Riccati differential equations) that describe the physics of thermal dark-matter-relic abundances. Two different asymptotic techniques are used, boundary-layer theory, which makes use of asymptotic matching, and the delta expansion, which is a powerful technique for solving nonlinear differential equations. Two different Boltzmann equations are considered. The first is derived from general relativistic considerations and the second arises in dilatonic string cosmology. The global asymptotic analysis presented here is used to find the long-time behavior of the solutions to these equations. In the first case the nature of the so-called freeze-out region and the post-freeze-out behavior is explored. In the second case the effect of the dilaton on cold dark-matter abundances is calculated and it is shown that there is a large-time power-law fall off of the dark-matter abundance. Corrections to the power-law behavior are also calculated.

14 citations

Journal ArticleDOI
TL;DR: In this paper, the authors proposed a new model to obtain asymptotic distributions near zero and compute the limiting distribution for the Ornstein-Uhlenbeck process driven by a fractional Brownian motion.
Abstract: Consider an Ornstein-Uhlenbeck process driven by a fractional Brownian motion. It is an interesting problem to find criteria for whether the process is stable or has a unit root, given a finite sample of observations. Recently, various asymptotic distributions for estimators of the drift parameter have been developed. We illustrate through computer simulations and through a Stein's bound that these asymptotic distributions are inadequate approximations of the finite-sample distribution for moderate values of the drift and the sample size. We propose a new model to obtain asymptotic distributions near zero and compute the limiting distribution. We show applications to regression analysis and obtain hypothesis tests and their asymptotic power.

14 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526