On the invariance principle for integrals of the shot noise processes (Q2777837)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the invariance principle for integrals of the shot noise processes |
scientific article; zbMATH DE number 1718882
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the invariance principle for integrals of the shot noise processes |
scientific article; zbMATH DE number 1718882 |
Statements
13 March 2002
0 references
invariance principle
0 references
shot noise process
0 references
0.8982601
0 references
0.8966958
0 references
0.89340687
0 references
0.8883996
0 references
On the invariance principle for integrals of the shot noise processes (English)
0 references
The author considers the stationary shot noise process \(\theta(u)=\int_{-\infty}^{+\infty}g(u-s) d\zeta(s)\), where \(\zeta(s)\) is a Lévy process and \(g(u)\in L_2(\mathbb R)\) is a response function. Let \(\Theta_T(t)=\int_0^{tT}\theta(u) du\), \(t\in[0,1]\). The convergence in law is proved of the normed random processes \(\Theta_T(t)\Bigl /\sqrt{E\Theta^2_T(1)}\) as \(T\to\infty\) to the fractional Brownian motion in the Banach space \(C[0,1]\).
0 references
