Homogeneous mappings of regularly varying vectors
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Homogeneous mappings of regularly varying vectors. / Dyszewski, Piotr; Mikosch, Thomas.
I: Annals of Applied Probability, Bind 30, Nr. 6, 2020, s. 2999-3026.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Homogeneous mappings of regularly varying vectors
AU - Dyszewski, Piotr
AU - Mikosch, Thomas
PY - 2020
Y1 - 2020
N2 - It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation property of product-type functions of regularly varying random vectors, generalizing and extending the univariate theory in various directions. The main result is then applied to characterize the regular variation property of products of i.i.d. regularly varying quadratic random matrices and of solutions to affine stochastic recurrence equations under nonstandard conditions.
AB - It is well known that the product of two independent regularly varying random variables with the same tail index is again regularly varying with this index. In this paper, we provide sharp sufficient conditions for the regular variation property of product-type functions of regularly varying random vectors, generalizing and extending the univariate theory in various directions. The main result is then applied to characterize the regular variation property of products of i.i.d. regularly varying quadratic random matrices and of solutions to affine stochastic recurrence equations under nonstandard conditions.
U2 - 10.1214/20-AAP1579
DO - 10.1214/20-AAP1579
M3 - Journal article
VL - 30
SP - 2999
EP - 3026
JO - Annals of Applied Probability
JF - Annals of Applied Probability
SN - 1050-5164
IS - 6
ER -
ID: 257649430