Weak stability and generalized weak convolution for random vectors and stochastic processes
| dc.creator | Misiewicz, Jolanta K. | |
| dc.date | 2006-08-09 | |
| dc.date.accessioned | 2026-07-07T07:21:35Z | |
| dc.date.available | 2026-07-07T07:21:35Z | |
| dc.description | A random vector ${\bf X}$ is weakly stable iff for all $a,b\in \mathbb{R}$ there exists a random variable $Θ$ such that $a{\bf X}+b{\bf X}'\stackrel{d}{=}{\bf X}Θ$. This is equivalent (see \cite{MOU}) with the condition that for all random variables $Q_1,Q_2$ there exists a random variable $Θ$ such that $$ X Q_1 + X' Q_2 \stackrel{d}{=} X Θ, $$ where ${\bf X},{\bf X}',Q_1,Q_2,Θ$ are independent. In this paper we define generalized convolution of measures defined by the formula $$ L(Q_1) \oplus_μ L(Q_2) = L(Θ), $$ if the equation $(*)$ holds for ${\bf X},Q_1,Q_2,Θ$ and $μ={\cal L}(Θ)$. We study here basic properties of this convolution, basic properties of $\oplus_μ$-infinitely divisible distributions, $\oplus_μ$-stable distributions and give a series of examples. | |
| dc.description | Published at http://dx.doi.org/10.1214/074921706000000149 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math/0608225 | |
| dc.identifier | http://arxiv.org/abs/math/0608225 | |
| dc.identifier | IMS Lecture Notes--Monograph Series 2006, Vol. 48, 109-118 | |
| dc.identifier | doi:10.1214/074921706000000149 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115349 | |
| dc.subject | Probability | |
| dc.subject | 60A10, 60B05, 60E05, 60E07, 60E10 (Primary) | |
| dc.title | Weak stability and generalized weak convolution for random vectors and stochastic processes | |
| dc.type | text |