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Very slowly varying functions - II
, 2007 This paper is a sequel to both Ash, Erdös and Rubel AER, on very slowly varying functions, and BOst1, on foundations of regular variation. We show that generalizations of the Ash-Erdös-Rubel approach -- imposing growth restrictions on the function h ...
Ostaszewski, Adam, Bingham, N. H.
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Differences of Slowly Varying Functions
Journal of Mathematical Analysis and Applications, 2000 A positive non-decreasing function \(F\) belongs to the class \(\text{O}\Pi^+\) if \(\limsup(t\to\infty)(F(st)- F(t))= M(s)\) is finite for every \(s> 1\). Given a non-decreasing slowly varying function \(L\), if, whenever it is written as a sum \(L= F+G\) of two non-decreasing functions, both \(F\) and \(G\) are slowly varying, \(L\) is said to have ...
Janković, Slobodanka +1 more
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Mathematics, 2023 In this paper we study the Marcinkiewicz–Zygmund-type strong law of large numbers with general normalizing sequences under sublinear expectation. Specifically, we establish complete convergence in the Marcinkiewicz–Zygmund-type strong law of large ...
Shuxia Guo, Zhe Meng
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Strong Convergence Bound of the Pareto Index Estimator under Right Censoring
Journal of Inequalities and Applications, 2010 Let {Xn,n≥1} be a sequence of positive independent and identically distributed random variables with common Pareto-type distribution function F(x)=1−x−1/γlF(x) as γ>0, where lF(x) represents a slowly varying ...
Bao Tao, Zuoxiang Peng
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Compact embeddings of Besov spaces involving only slowly varying smoothness [PDF]
, 2011 summary:We characterize compact embeddings of Besov spaces $B^{0,b}_{p,r}(\mathbb {R}^n)$ involving the zero classical smoothness and a slowly varying smoothness $b$ into Lorentz-Karamata spaces $L_{p, q; \bar {b}}(\Omega )$, where $\Omega $ is a bounded
Opic, Bohumír +2 more
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Electronic Journal of Qualitative Theory of Differential Equations, 2012 The asymptotic behavior of solutions of the odd-order differential equation of Emden-Fowler type $$ x^{(2n+1)}(t) + q(t)|x(t)|^{\gamma}\textrm{sgn}\;x(t)=0 , $$ is studied in the framework of regular variation, under the assumptions that ...
Takaŝi Kusano, Jelena Manojlović
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Aequationes Mathematicae, 1972 Let \(\varphi\) be a positive non-decreasing real valued function defined on \([0, \infty)\), and let \(f\) be any real valued function defined on \([0, \infty)\). We say that \(f\) is \(\varphi\)-slowly varying if \(\varphi (x)[f(x+ \alpha)-f(x)] \to 0\) as \(x \to \infty\) for each \(\alpha\). We say that \(f\) is uniformly \(\varphi\)-slowly varying
Erdös, P. +2 more
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Long extra-tropical planetary wave propagation in the presence of slowly varying mean flow and bottom topography. II: ray propagation and comparison with observations [PDF]
, 2003 Ray theory is used to predict phase and group velocities for long planetary waves under realistic, albeit slowly varying, oceanic conditions. The results are compared with local theory using fields smoothed to the same amount (9° latitude/longitude) as ...
Killworth, Peter D. +8 more
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Large Deviation Results and Applications to the Generalized Cramér Model
Mathematics, 2018 In this paper, we prove large deviation results for some sequences of weighted sums of random variables. These sequences have applications to the probabilistic generalized Cramér model for products of primes in arithmetic progressions; they could lead to
Rita Giuliano, Claudio Macci
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Identifiability of slowly varying systems [PDF]
, 1976 A system is conceived of as being slowly varying if it changes slowly enough to permit identification to within a specified error. A generic model is developed to study the identifiability and identification of slowly varying systems.
Fiske, Philip Howard., Root, William L.
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