Heavy tailed solutions of multivariate smoothing transforms

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:123

Article

Buraczewski, Dariusz¹  Damek, Ewa¹  Mentemeier, Sebastian²  Mirek, Mariusz¹ 

[1] Uniwersytet Wroclawski, Inst Matemat, PL-50384 Wroclaw, Poland

[2] Univ Munster, Inst Stat Math, D-48149 Munster, Germany

关键词: Distributions;    General theory;    Renewal theory;    Branching;   

DOI  :  10.1016/j.spa.2013.02.003

来源: Elsevier

【 摘 要 】

Let N > 1 be a fixed integer and (C-1, ... , C-N, Q) a random element of M (d x d, R)(N) x R-d. We consider solutions of multivariate smoothing transforms, i.e. random variables R satisfying R =(d) Sigma(i=1CiRi)-C-N + Q where =(d) denotes equality in distribution, and R, R-1, .. , R-N are independent identically distributed R-d-valued random variables, and independent of (C-1, ..., C-N, Q). We briefly review conditions for the existence of solutions, and then study their asymptotic behaviour. We show that under natural conditions, these solutions exhibit heavy tails. Our results also cover the case of complex valued weights (C-1, ... , C-N). (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free