scholarly journals REGULAR VARIATION AND STABILITY OF RANDOM MEASURES

2017 ◽  
Vol 54 (3) ◽  
pp. 1049-1061
Author(s):  
Nam Bui Quang ◽  
Phuc Ho Dang
Keyword(s):  
Regular Variation ◽  
Random Measures

Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kusano Takaŝi ◽  
Jelena V. Manojlović
Keyword(s):  
Differential Equation ◽  
Asymptotic Behavior ◽  
Continuous Function ◽  
Differential Equations ◽  
Linear Differential Equation ◽  
Regular Variation ◽  
Asymptotic Formulas ◽  
Asymptotic Behavior Of Solutions ◽  
Positive Continuous Function ◽  
Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

Point processes, regular variation and weak convergence

1986 ◽  
Vol 18 (01) ◽  
pp. 66-138 ◽  
Author(s):  
Sidney I. Resnick
Keyword(s):  
Weak Convergence ◽  
Function Space ◽  
Regular Variation ◽  
Point Processes ◽  
Sufficient Condition ◽  
Space Setting

A method is reviewed for proving weak convergence in a function-space setting when regular variation is a sufficient condition. Point processes and weak convergence techniques involving continuity arguments play a central role. The method is dimensionless and holds computations to a minimum. Many applications of the methods to processes derived from sums and maxima are given.

Exchangeable random measures in the plane

1990 ◽  
Vol 3 (1) ◽  
pp. 81-136 ◽  
Author(s):  
Olav Kallenberg
Keyword(s):  
Random Measures
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