Slowly varying functions and asymptotic relations
نویسندگان
چکیده
منابع مشابه
Very Slowly Varying Functions
A real-valued function f of a real variable is said to be (p-slowly varying ((p-s .v.) if limn_ . rp (x) [ f (x + a) f (x)] = 0 for each a. It is said to be uniformly 9-slowly varying (u . (P-s .v .) if limn-. . sup, e r rp(x) ; f (x-a) f (x)I =0 for every bounded interval I. It is supposed throughout that rp is positive and increasing . It is proved that if w increases rapidly enough, then eve...
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This paper is a sequel to both Ash, Erd1⁄2os and Rubel [AER], on very slowly varying functions, and [BOst1], on foundations of regular variation. We show that generalizations of the Ash-Erd1⁄2os-Rubel approach imposing growth restrictions on the function h, rather than regularity conditions such as measurability or the Baire property lead naturally to the main result of regular variation, th...
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Asymptotic behavior of the OLS estimator for regressions with two slowly varying regressors is studied. It is shown that the asymptotic distribution may belong to one of four types depending on the relative rates of growth of the regressors. The paper expands and corrects recent results by P.C.B.Phillips (2007).
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Let L(x) be a slowly varying function at both zero and infinity. The existence of the non-commutative neutrix convolution product of the distributions x+L(x) and x μ − is proved, where λ, μ are real numbers such that λ, μ / ∈ −N and λ+μ / ∈ −Z . Some other products of distributions are obtained. AMS Mathematics Subject Classification (2000): 46F10
متن کاملFurther results on Lyapunov functions for slowly time-varying systems
We provide general methods for explicitly constructing strict Lyapunov functions for fully nonlinear slowly time-varying systems. Our results apply to cases where the given dynamics and corresponding frozen dynamics are not necessarily exponentially stable. This complements our previous Lyapunov function constructions for rapidly time-varying dynamics. We also explicitly construct input-to-stat...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1971
ISSN: 0022-247X
DOI: 10.1016/0022-247x(71)90114-4