Geodesic
On the strong Brillinger-mixing property of ${\alpha }$-determinantal point processes and some applications
Applications of Mathematics, Tome 61 (2016) no. 4, pp. 443-461

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

First, we derive a representation formula for all cumulant density functions in terms of the non-negative definite kernel function $C(x,y)$ defining an ${\alpha }$-determinantal point process (DPP). Assuming absolute integrability of the function $C_0(x) = C(o,x)$, we show that a stationary ${\alpha }$-DPP with kernel function $C_0(x)$ is ``strongly'' Brillinger-mixing, implying, among others, that its tail-$\sigma $-field is trivial. Second, we use this mixing property to prove rates of normal convergence for shot-noise processes and sketch some applications to statistical second-order analysis of ${\alpha }$-DPPs.
DOI : 10.1007/s10492-016-0141-y
Classification : 60F05, 60G55
Keywords: determinantal point process; permanental point process; trivial tail-$\sigma $-field; exponential moment; shot-noise process; Berry-Esseen bound; multiparameter $K$-function; kernel-type product density estimator; goodness-of-fit test 
@article{10_1007_s10492_016_0141_y,
     author = {Heinrich, Lothar},
     title = {On the strong {Brillinger-mixing} property of ${\alpha }$-determinantal point processes and some applications},
     journal = {Applications of Mathematics},
     pages = {443--461},
     publisher = {mathdoc},
     volume = {61},
     number = {4},
     year = {2016},
     doi = {10.1007/s10492-016-0141-y},
     mrnumber = {3532253},
     zbl = {06644006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0141-y/}
}
TY  - JOUR
AU  - Heinrich, Lothar
TI  - On the strong Brillinger-mixing property of ${\alpha }$-determinantal point processes and some applications
JO  - Applications of Mathematics
PY  - 2016
SP  - 443
EP  - 461
VL  - 61
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0141-y/
DO  - 10.1007/s10492-016-0141-y
LA  - en
ID  - 10_1007_s10492_016_0141_y
ER  - 
%0 Journal Article
%A Heinrich, Lothar
%T On the strong Brillinger-mixing property of ${\alpha }$-determinantal point processes and some applications
%J Applications of Mathematics
%D 2016
%P 443-461
%V 61
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1007/s10492-016-0141-y/
%R 10.1007/s10492-016-0141-y
%G en
%F 10_1007_s10492_016_0141_y
Heinrich, Lothar. On the strong Brillinger-mixing property of ${\alpha }$-determinantal point processes and some applications. Applications of Mathematics, Tome 61 (2016) no. 4, pp. 443-461. doi: 10.1007/s10492-016-0141-y

Cité par Sources :