Estimating intensity functions of spatial inhomogeneous Poisson point processes via a Stein estimator

2021 ◽  
pp. 1-33
Author(s):  
Yujiao Lu ◽  
Wanyang Dai
Keyword(s):  
Point Processes ◽  
Poisson Point Processes ◽  
Stein Estimator ◽  
Intensity Functions

scholarly journals Isomorphisms between determinantal point processes with translation-invariant kernels and Poisson point processes

2020 ◽  
pp. 1-14
Author(s):  
SHOTA OSADA
Keyword(s):  
Point Processes ◽  
Duke Math ◽  
Random Point ◽  
Determinantal Point Processes ◽  
Fredholm Determinants ◽  
Poisson Point Processes ◽  
Translation Invariant ◽  
Ergodic Properties ◽  
Tree Representations ◽  
Invariant Kernels

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.

scholarly journals A generalization of Matérn hard-core processes with applications to max-stable processes

2020 ◽  
Vol 57 (4) ◽  
pp. 1298-1312
Author(s):  
Martin Dirrler ◽  
Christopher Dörr ◽  
Martin Schlather
Keyword(s):  
Point Process ◽  
Point Processes ◽  
Hard Core ◽  
Domain Of Attraction ◽  
Stable Processes ◽  
Poisson Point Processes ◽  
Original Process ◽  
Mixed Moving Maxima

AbstractMatérn hard-core processes are classical examples for point processes obtained by dependent thinning of (marked) Poisson point processes. We present a generalization of the Matérn models which encompasses recent extensions of the original Matérn hard-core processes. It generalizes the underlying point process, the thinning rule, and the marks attached to the original process. Based on our model, we introduce processes with a clear interpretation in the context of max-stable processes. In particular, we prove that one of these processes lies in the max-domain of attraction of a mixed moving maxima process.

Bayesian modeling and decision theory for non-homogeneous Poisson point processes

2020 ◽  
Vol 36 ◽  
pp. 100412
Author(s):  
Jiaxun Chen ◽  
Athanasios C. Micheas ◽  
Scott H. Holan
Keyword(s):  
Decision Theory ◽  
Bayesian Modeling ◽  
Point Processes ◽  
Poisson Point Processes

scholarly journals The Cauchy–Schwarz Divergence for Poisson Point Processes

2015 ◽  
Vol 61 (8) ◽  
pp. 4475-4485 ◽  
Author(s):  
Hung Gia Hoang ◽  
Ba-Ngu Vo ◽  
Ba-Tuong Vo ◽  
Ronald Mahler
Keyword(s):  
Point Processes ◽  
Poisson Point Processes

A note on disjoint-occurrence inequalities for marked Poisson point processes

1996 ◽  
Vol 33 (2) ◽  
pp. 420-426 ◽  
Author(s):  
J. van den Berg
Keyword(s):  
Weak Convergence ◽  
Point Processes ◽  
Poisson Point Processes ◽  
Bk Inequality

For (marked) Poisson point processes we give, for increasing events, a new proof of the analog of the BK inequality. In contrast to other proofs, which use weak-convergence arguments, our proof is ‘direct' and requires no extra topological conditions on the events. Apart from some well-known properties of Poisson point processes, the proof is self-contained.

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