q‐regular variation and the existence of solutions of half‐linear q‐difference equation
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DOI: 10.1002/mma.7570
Abstract: The half‐linear q‐difference equation Dq(p(t)Φ(Dq(x(t))))+r(t)Φ(x(qt))=0,t∈qℕ0={qn:n∈ℕ0},q>1, where Φ(x)=|x|αsgnx , α>0,p:qℕ0→(0,∞),r:qℕ0→ℝ , is analyzed in the framework of q‐regular variation. Necessary and sufficient conditions for the existence of q‐regularly varying solutions are given, under the assumption that… read more here.
Keywords: regular variation; half linear; linear difference; difference equation ... See more keywords
Asymptotics of convolution with the semi-regular-variation tail and its application to risk
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DOI: 10.1007/s10687-018-0326-8
Abstract: In this paper, according to a certain criterion, we divide the exponential distribution class into some subclasses. One of them is closely related to the regular-variation-tailed distribution class, and is called the semi-regular-variation-tailed distribution class.… read more here.
Keywords: semi regular; class; regular variation; convolution ... See more keywords
A formula for hidden regular variation behavior for symmetric stable distributions
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DOI: 10.1007/s10687-020-00381-4
Abstract: We develop a formula for the power-law decay of various sets for symmetric stable random vectors in terms of how many vectors from the support of the corresponding spectral measure are needed to enter the… read more here.
Keywords: regular variation; symmetric stable; hidden regular; formula hidden ... See more keywords