| Title:
|
Central limit theorem for Gibbsian U-statistics of facet processes (English) |
| Author:
|
Večeřa, Jakub |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
423-441 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A special case of a Gibbsian facet process on a fixed window with a discrete orientation distribution and with increasing intensity of the underlying Poisson process is studied. All asymptotic joint moments for interaction U-statistics are calculated and the central limit theorem is derived using the method of moments. (English) |
| Keyword:
|
central limit theorem |
| Keyword:
|
facet process |
| Keyword:
|
U-statistics |
| MSC:
|
60D05 |
| MSC:
|
60G55 |
| idZBL:
|
Zbl 06644005 |
| idMR:
|
MR3532252 |
| DOI:
|
10.1007/s10492-016-0140-z |
| . |
| Date available:
|
2016-08-01T09:25:09Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145794 |
| . |
| Reference:
|
[1] Beneš, V., M.Zikmundová: Functionals of spatial point processes having a density with respect to the Poisson process.Kybernetika 50 896-913 (2014). MR 3301778 |
| Reference:
|
[2] Billingsley, P.: Probability and Measure.John Wiley & Sons, New York (1995). Zbl 0822.60002, MR 1324786 |
| Reference:
|
[3] Georgii, H.-O., Yoo, H. J.: Conditional intensity and Gibbsianness of determinantal point processes.J. Stat. Phys. 118 55-84 (2005). Zbl 1130.82016, MR 2122549, 10.1007/s10955-004-8777-5 |
| Reference:
|
[4] Last, G., Penrose, M. D.: Poisson process Fock space representation, chaos expansion and covariance inequalities.Probab. Theory Relat. Fields 150 663-690 (2011). Zbl 1233.60026, MR 2824870, 10.1007/s00440-010-0288-5 |
| Reference:
|
[5] Last, G., Penrose, M. D., Schulte, M., Thäle, C.: Moments and central limit theorems for some multivariate Poisson functionals.Adv. Appl. Probab. 46 (2014), 348-364. Zbl 1350.60020, MR 3215537, 10.1017/S0001867800007126 |
| Reference:
|
[6] Peccati, G., Taqqu, M. S.: Wiener chaos: Moments, Cumulants and Diagrams. A survey with computer implementation.Bocconi University Press, Milano; Springer, Milan (2011). Zbl 1231.60003, MR 2791919 |
| Reference:
|
[7] Reitzner, M., Schulte, M.: Central limit theorems for $U$-statistics of Poisson point processes.Ann. Probab. 41 (2013), 3879-3909. Zbl 1293.60061, MR 3161465, 10.1214/12-AOP817 |
| Reference:
|
[8] Schreiber, T., Yukich, J. E.: Limit theorems for geometric functionals of Gibbs point processes.Ann. Inst. Henri Poincaré, Probab. Stat. 49 (2013), 1158-1182. Zbl 1308.60064, MR 3127918, 10.1214/12-AIHP500 |
| Reference:
|
[9] Večeřa, J., Beneš, V.: Interaction processes for unions of facets, the asymptotic behaviour with increasing intensity.Methodol. Comput. Appl. Probab. DOI-10.1007/s11009-016-9485-8 (2016). Zbl 1370.60015, MR 3564860, 10.1007/s11009-016-9485-8 |
| . |
