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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01 Jan 2016TL;DR: In this article, the authors present an asymptotic expansion of a martingale with a asmptotically mixed normal distribution, where the expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard invariance principle.
Abstract: The quasi-likelihood estimator and the Bayesian type estimator of the volatility parameter are in general asymptotically mixed normal. In case the limit is normal, the asymptotic expansion was derived in Yoshida 1997 as an application of the martingale expansion. The expansion for the asymptotically mixed normal distribution is then indispensable to develop the higher-order approximation and inference for the volatility. The classical approaches in limit theorems, where the limit is a process with independent increments or a simple mixture, do not work. We present asymptotic expansion of a martingale with asymptotically mixed normal distribution. The expansion formula is expressed by the adjoint of a random symbol with coefficients described by the Malliavin calculus, differently from the standard invariance principle. Applications to a quadratic form of a diffusion process (“realized volatility”) is discussed.
8 citations
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01 Jan 1994TL;DR: In this article, the role of asymptotics in a variety of fields, most of which are related to mechanics but are not restricted to fluids, is discussed and discussed.
Abstract: This is not a review paper. It is, rather, a collection of thoughts on the role of asymptotics in a variety of fields, most of which are related to mechanics but are not restricted to fluids. The emphasis is more on the achievements of asymptotics, than on the description of the methods used to achieve these. The topics have been chosen so as to illustrate the versatility of asymptotic methods concerning the type of problems solved and the degree of sophistication required by each particular solution. No internal logic other than that illustrating this efficiency and versatility should be expected in this paper.
8 citations
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8 citations
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TL;DR: In this article, the authors formulated the definition of the asymptotic expansion of a generalized function depending on a parameter and proved a number of theorems about the properties of such expansions and operations.
Abstract: The definition is formulated of the asymptotic expansion of a generalized function depending on a parameter. A number of theorems are proved about the properties of asymptotic expansions and operations on them, in particular, theorems on differentiation and integration. For generalized functions of the formf (x)eixt,f (x) ɛS', t → ±∞ the relation is investigated between the singularity carrierf and the carrier of coefficient functionals.
8 citations