scholarly journals Periodic moving averages of random variables with regularly varying tails

1997 ◽  
Vol 25 (2) ◽  
pp. 771-785 ◽  
Author(s):  
Paul L. Anderson ◽  
Mark M. Meerschaert
Keyword(s):  
Random Variables ◽  
Moving Averages ◽  
Regularly Varying

scholarly journals On a Theorem of Breiman and a Class of Random Difference Equations

2007 ◽  
Vol 44 (04) ◽  
pp. 1031-1046 ◽  
Author(s):  
Denis Denisov ◽  
Bert Zwart
Keyword(s):  
Difference Equations ◽  
Random Variables ◽  
Tail Behavior ◽  
Random Difference ◽  
Regularly Varying ◽  
Random Difference Equations

We consider the tail behavior of the product of two independent nonnegative random variables X and Y. Breiman (1965) has considered this problem, assuming that X is regularly varying with index α and that E{Yα+ε} < ∞ for some ε > 0. We investigate when the condition on Y can be weakened and apply our findings to analyze a class of random difference equations.

Expected number of real zeroes of random Taylor series

2019 ◽  
Vol 22 (07) ◽  
pp. 1950059
Author(s):  
Hendrik Flasche ◽  
Zakhar Kabluchko
Keyword(s):  
Taylor Series ◽  
Random Variables ◽  
Index Formula ◽  
Real Sequence ◽  
Expected Number ◽  
Unit Variance ◽  
Regularly Varying

Let [Formula: see text] be i.i.d. random variables with zero mean and unit variance. Consider a random Taylor series of the form [Formula: see text] where [Formula: see text] is a real sequence such that [Formula: see text] is regularly varying with index [Formula: see text], where [Formula: see text]. We prove that [Formula: see text] where [Formula: see text] denotes the number of real zeroes of [Formula: see text] in the interval [Formula: see text].

scholarly journals Tail Approximations for Sums of Dependent Regularly Varying Random Variables Under Archimedean Copula Models

2018 ◽  
Vol 21 (2) ◽  
pp. 461-490 ◽  
Author(s):  
Hélène Cossette ◽  
Etienne Marceau ◽  
Quang Huy Nguyen ◽  
Christian Y. Robert
Keyword(s):  
Random Variables ◽  
Archimedean Copula ◽  
Copula Models ◽  
Regularly Varying

scholarly journals On closure and factorization properties of subexponential and related distributions

1980 ◽  
Vol 29 (2) ◽  
pp. 243-256 ◽  
Author(s):  
Paul Embrechts ◽  
Charles M. Goldie
Keyword(s):  
Distribution Function ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Regularly Varying

AbstractFor a distribution function F on [0, ∞] we say F ∈ if {1 – F(2)(x)}/{1 – F(x)}→2 as x→∞, and F∈, if for some fixed γ > 0, and for each real , limx→∞ {1 – F(x + y)}/{1 – F(x)} ═ e– n. Sufficient conditions are given for the statement F ∈ F * G ∈ and when both F and G are in y it is proved that F*G∈pF + 1(1 – p) G ∈ for some (all) p ∈(0,1). The related classes ℒt are proved closed under convolutions, which implies the closure of the class of positive random variables with regularly varying tails under multiplication (of random variables). An example is given that shows to be a proper subclass of ℒ 0.

scholarly journals Moving Averages of Random Vectors with Regularly Varying Tails

2000 ◽  
Vol 21 (3) ◽  
pp. 297-328 ◽  
Author(s):  
Mark M. Meerschaert ◽  
Hans-Peter Scheffler
Keyword(s):  
Moving Averages ◽  
Random Vectors ◽  
Regularly Varying

scholarly journals Hidden regular variation of moving average processes with heavy-tailed innovations

2014 ◽  
Vol 51 (A) ◽  
pp. 267-279 ◽  
Author(s):  
Sidney I. Resnick ◽  
Joyjit Roy
Keyword(s):  
Sequence Space ◽  
Regular Variation ◽  
Moving Average ◽  
Random Variables ◽  
Continuity Properties ◽  
Hidden Regular Variation ◽  
Constant Coefficients ◽  
Moving Average Processes ◽  
Regularly Varying ◽  
Heavy Tailed

We look at joint regular variation properties of MA(∞) processes of the form X = (Xk, k ∈ Z), where Xk = ∑j=0∞ψjZk-j and the sequence of random variables (Zi, i ∈ Z) are independent and identically distributed with regularly varying tails. We use the setup of MO-convergence and obtain hidden regular variation properties for X under summability conditions on the constant coefficients (ψj: j ≥ 0). Our approach emphasizes continuity properties of mappings and produces regular variation in sequence space.

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