| Title:
|
On the strong Brillinger-mixing property of ${\alpha }$-determinantal point processes and some applications (English) |
| Author:
|
Heinrich, Lothar |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
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61 |
| Issue:
|
4 |
| Year:
|
2016 |
| Pages:
|
443-461 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
determinantal point process |
| Keyword:
|
permanental point process |
| Keyword:
|
trivial tail-$\sigma $-field |
| Keyword:
|
exponential moment |
| Keyword:
|
shot-noise process |
| Keyword:
|
Berry-Esseen bound |
| Keyword:
|
multiparameter $K$-function |
| Keyword:
|
kernel-type product density estimator |
| Keyword:
|
goodness-of-fit test |
| MSC:
|
60F05 |
| MSC:
|
60G55 |
| idZBL:
|
Zbl 06644006 |
| idMR:
|
MR3532253 |
| DOI:
|
10.1007/s10492-016-0141-y |
| . |
| Date available:
|
2016-08-01T09:27:08Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/145795 |
| . |
| Reference:
|
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