| Title:
|
Mean quadratic convergence of signed random measures (English) |
| Author:
|
Jacob, P. |
| Author:
|
Oliveira, P. E. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
32 |
| Issue:
|
1 |
| Year:
|
1991 |
| Pages:
|
119-123 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider signed Radon random measures on a separable, complete and locally compact metric space and study mean quadratic convergence with respect to vague topology on the space of measures. We prove sufficient conditions in order to obtain mean quadratic convergence. These results are based on some identification properties of signed Radon measures on the product space, also proved in this paper. (English) |
| Keyword:
|
relative compactness; mean quadratic convergence |
| MSC:
|
28A20 |
| MSC:
|
28C05 |
| MSC:
|
60B10 |
| MSC:
|
60F25 |
| MSC:
|
60G57 |
| idZBL:
|
Zbl 0731.60030 |
| idMR:
|
MR1118295 |
| . |
| Date available:
|
2008-10-09T13:11:21Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/116948 |
| . |
| Reference:
|
[1] Billingsley P.: Convergence of Probability Measures.John Wiley & Sons, 1968. Zbl 0944.60003, MR 0233396 |
| Reference:
|
[2] Bonkian S.M.: Contribution à l'étude des mesures aléatoires du second ordre.Thèse du 3$^{ {ème}}$ cycle, Université des Sciences et Techniques de Lille I, 1983. |
| Reference:
|
[3] Halmos P.R.: Measure Theory.D. Van Nostrand Co. Inc., Princeton, New Jersey, 1950. Zbl 0283.28001, MR 0033869 |
| Reference:
|
[4] Jacob P.: Convergence uniforme à distance finie de mesures signées.Ann. Inst. Henri Poincaré, 15 (1979), n$^{ o}$4, 355-373. Zbl 0439.60006, MR 0567733 |
| Reference:
|
[5] Kallenberg O.: Random Measures.Academic Press, 1976. Zbl 0694.60030, MR 0431373 |
| Reference:
|
[6] Lima E.L.: Espaços métricos.Projecto Euclides, IMPA, Rio de Janeiro, 1983. Zbl 0529.54001 |
| Reference:
|
[7] Marle C.-M.: Mesures et Probabilités.Enseignement des Sciences, Hermann, Paris, 1974. Zbl 0306.28001, MR 0486378 |
| Reference:
|
[8] Oliveira P.E.: Convergence de suite de mesures et convergence des masses.Pub. IRMA, Lille, 13 (1988), II. |
| Reference:
|
[9] Tortrat A.: Calcul des probabilités et introduction aux processus aléatoires.Masson, Paris, 1971. Zbl 0212.49201, MR 0375403 |
| Reference:
|
[10] Varadarajan V.S.: Measures on Topological Spaces.Transl. of Ame. Math. Soc., Series 2, 48 (1965), 161-228. |
| . |
