| Title:
|
Linear rescaling of the stochastic process (English) |
| Author:
|
Lachout, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
277-289 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Discussion on the limits in distribution of processes $Y$ under joint rescaling of space and time is presented in this paper. The results due to Lamperti (1962), Weissman (1975), Hudson & Mason (1982) and Laha & Rohatgi (1982) are improved here. (English) |
| Keyword:
|
self-similar processes |
| Keyword:
|
convergence in distribution |
| MSC:
|
60F05 |
| MSC:
|
60G10 |
| MSC:
|
60G18 |
| MSC:
|
60G99 |
| MSC:
|
62E10 |
| MSC:
|
62E20 |
| idZBL:
|
Zbl 0757.60034 |
| idMR:
|
MR1189658 |
| . |
| Date available:
|
2009-01-08T17:55:37Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118495 |
| . |
| Reference:
|
[1] Aczél J.: Lectures on Functional Equations and their Applications.Academic Press, New York, 1966. MR 0208210 |
| Reference:
|
[2] Hudson W.H., Mason J.D.: Operator-self-similar processes in a finite-dimensional space.Trans. AMS 273 (1982), 281-297. Zbl 0508.60044, MR 0664042 |
| Reference:
|
[3] Jarník V.: Differential Calculus II (in Czech).Academia, Prague, 1976. |
| Reference:
|
[4] Laha R.G., Rohatgi V.K.: Operator self similar stochastic processes in $R_+^d$.Stochastic Process. Appl. 12 (1982), 73-84. MR 0632393 |
| Reference:
|
[5] Lamperti J.: Semi-stable stochastic processes.Trans. Amer. Math. Soc. 104 (1962), 62-78. Zbl 0286.60017, MR 0138128 |
| Reference:
|
[6] Vervaat W.: Properties of General Self-Similar Processes.46th Session of the International Statistical Institute of Tokyo, Japan, 1987. Zbl 0813.60041, MR 1027195 |
| Reference:
|
[7] Weissman I.: On location and scale functions of a class of limiting processes with application to extreme value theory.Ann. Probab. 3 (1975), 178-181. Zbl 0303.60021, MR 0362458 |
| . |
