Autor:	Damek, Ewa, Zienkiewicz, Jacek
Rok vydání:	2018
Předmět:	Mathematics - Probability
Zdroj:	Journal of Difference Equations and Applications, 2018
Druh dokumentu:	Working Paper
DOI:	10.1080/10236198.2017.1422249.
Popis:	We study solution X of the stochastic equation X = AX +B, where A is a random matrix and B,X are random vectors, the law of (A,B) is given and X is independent of (A,B). The equation is meant in law, the matrix A is 2x2 upper triangular, A_{11}=A_{22}>0, A_{12} is real. A sharp asymptotics of the tail of X =(X _1,X_2) is obtained. We show that under "so called" Kesten-Goldie conditions P (X_2>t)\sim t^{-a} and P (X_1>t )\sim t^{-a}(\log t)^b, where b =a or a\2.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1806.08985 Zobrazit plný text záznamu View this record from Arxiv