Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
central limit theorem; facet process; U-statistics
central limit theorem; facet process; U-statistics
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.
References:
[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
[2] Billingsley, P.: Probability and Measure. John Wiley & Sons, New York (1995). MR 1324786 | Zbl 0822.60002
[3] Georgii, H.-O., Yoo, H. J.: Conditional intensity and Gibbsianness of determinantal point processes. J. Stat. Phys. 118 55-84 (2005). DOI 10.1007/s10955-004-8777-5 | MR 2122549 | Zbl 1130.82016
[4] Last, G., Penrose, M. D.: Poisson process Fock space representation, chaos expansion and covariance inequalities. Probab. Theory Relat. Fields 150 663-690 (2011). DOI 10.1007/s00440-010-0288-5 | MR 2824870 | Zbl 1233.60026
[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. DOI 10.1017/S0001867800007126 | MR 3215537 | Zbl 1350.60020
[6] Peccati, G., Taqqu, M. S.: Wiener chaos: Moments, Cumulants and Diagrams. A survey with computer implementation. Bocconi University Press, Milano; Springer, Milan (2011). MR 2791919 | Zbl 1231.60003
[7] Reitzner, M., Schulte, M.: Central limit theorems for $U$-statistics of Poisson point processes. Ann. Probab. 41 (2013), 3879-3909. DOI 10.1214/12-AOP817 | MR 3161465 | Zbl 1293.60061
[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. DOI 10.1214/12-AIHP500 | MR 3127918 | Zbl 1308.60064
[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). DOI 10.1007/s11009-016-9485-8 | MR 3564860 | Zbl 1370.60015
Search
Partner of
