| Title |
Ribinis ilgosios atminties funkcinių tiesinių procesų elgesys / |
| Translation of Title |
Asymptotic behaviour of long memory functional linear processes. |
| Authors |
Characiejus, Vaidotas |
| Full Text |
|
| Pages |
26 |
| Keywords [eng] |
Linear process ; central limit theorem ; functional central limit theorem ; law of large numbers ; long memory |
| Abstract [eng] |
We investigate the asymptotic behaviour of linear processes. The interesting question is whether the asymptotic behaviour of the linear process differs from the asymptotic behaviour of independent and identically distributed random elements. By asymptotic behaviour we mean the convergence in some sense of the normalised partial sums and the normalised random polygonal lines. We investigate the central limit theorem and the functional central limit theorem for a particular functional linear process and the Marcinkiewicz-Zygmund type weak and strong laws of large numbers for a general linear process with values in a separable Hilbert space when the operators of the linear processes are not absolutely summable. The most interesting feature of the central limit theorem is that the normalising sequence is a sequence of multiplication operators. The limit Gaussian process of the functional central limit theorem generates an operator-self similar process. We establish that under the absolute summability of the operators of the linear process the Marcinkiewicz-Zygmund type weak and strong laws of large numbers hold with the standard normalising sequence, i.e. the same normalising sequence as in the case of independent and identically distributed random elements. However, if the operators of the linear process are not absolutely summable, then non-standard normalising sequence might be needed as we illustrate with an example. . |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Summaries of doctoral thesis |
| Language |
Lithuanian |
| Publication date |
2015 |
