2021 ◽  
Vol 58 (2) ◽  
pp. 469-483
Author(s):  
Jesper Møller ◽  
Eliza O’Reilly

AbstractFor a determinantal point process (DPP) X with a kernel K whose spectrum is strictly less than one, André Goldman has established a coupling to its reduced Palm process $X^u$ at a point u with $K(u,u)>0$ so that, almost surely, $X^u$ is obtained by removing a finite number of points from X. We sharpen this result, assuming weaker conditions and establishing that $X^u$ can be obtained by removing at most one point from X, where we specify the distribution of the difference $\xi_u: = X\setminus X^u$. This is used to discuss the degree of repulsiveness in DPPs in terms of $\xi_u$, including Ginibre point processes and other specific parametric models for DPPs.


1996 ◽  
Vol 33 (01) ◽  
pp. 57-70
Author(s):  
Bartłomiej Błaszczyszyn ◽  
Tomasz Rolski

Let N be a stationary Markov-modulated marked point process on ℝ with intensity β ∗ and consider a real-valued functional ψ(N). In this paper we study expansions of the form Eψ(N) = a 0 + β ∗ a 1 + ·· ·+ (β∗ ) nan + o((β ∗) n ) for β ∗→ 0. Formulas for the coefficients ai are derived in terms of factorial moment measures of N. We compute a 1 and a 2 for the probability of ruin φ u with initial capital u for the risk process in the Markov-modulated environment; a 0 = 0. Moreover, we give a sufficient condition for ϕu to be an analytic function of β ∗. We allow the premium rate function p(x) to depend on the actual risk reserve.


2013 ◽  
Vol 5 (4) ◽  
pp. 107-140 ◽  
Author(s):  
Tobias Broer

This paper shows how two standard models of consumption risk-sharing—self-insurance through borrowing and saving and limited commitment to insurance contracts—replicate similarly well the standard, second-moment measures of insurance observed in US micro data. A nonparametric analysis, however, reveals strongly contrasting and counterfactual joint distributions of consumption, income and wealth. Method of moments estimation shows how measurement error in consumption eliminates excessive skewness and smoothness of consumption growth. Moreover, counterfactual nonlinearities disappear at high-estimated risk aversion under self-insurance, but are a robust feature of limited commitment. Its “shape of insurance” thus argues in favor of the self-insurance model. (JEL D14, D81, D91, G22, E21)


2016 ◽  
Vol 44 (1) ◽  
pp. 192-203 ◽  
Author(s):  
Jean-François Coeurjolly ◽  
Jesper Møller ◽  
Rasmus Waagepetersen

2019 ◽  
Vol 146 (4) ◽  
pp. 2994-2994
Author(s):  
Hsin-Hua Chen ◽  
Yunying She ◽  
Yaoh-shiang Lin

1979 ◽  
Vol 16 (02) ◽  
pp. 261-273 ◽  
Author(s):  
Larry P. Ammann ◽  
Peter F. Thall

The probability generating functional (p.g.fl.) of a non-homogeneous Poisson cluster process is characterized in Ammann and Thall (1977) via a decomposition of the KLM measure of the process. This p.g.fl. representation is utilized in the present article to show that the family 𝒟 of Poisson cluster processes with a.s. finite clusters is invariant under a class of cluster transformations. Explicit expressions for the finite-dimensional count distributions, product moment measures, and the distribution of clusters are derived in terms of the KLM measure. It is also shown that an element of 𝒟 has no multiple events iff the points of each cluster are a.s. distinct.


1996 ◽  
Vol 28 (02) ◽  
pp. 335-336
Author(s):  
Kiên Kiêu ◽  
Marianne Mora

Random measures are commonly used to describe geometrical properties of random sets. Examples are given by the counting measure associated with a point process, and the curvature measures associated with a random set with a smooth boundary. We consider a random measure with an invariant distribution under the action of a standard transformation group (translatioris, rigid motions, translations along a given direction and so on). In the framework of the theory of invariant measure decomposition, the reduced moments of the random measure are obtained by decomposing the related moment measures.


Author(s):  
P. Avramidis ◽  
G. Iliopoulos ◽  
N. Kontopoulos ◽  
D. Panagiotaras ◽  
P. Barouchas ◽  
...  

ABSTRACTThis study presents sedimentological, palaeoecological and geochemical data from a shallow Mediterranean coastal lagoon which has been severely influenced by human intervention over the last 70 years. The Gialova Lagoon is protected by international conventions and is listed in the Natura 2000 European Community Network as Special Protection Area (SPA) and Site of Community Importance (SCI). The spatial variability of sediment characteristics such as grain size, total organic carbon (TOC) and moment measures, mean, sorting, kurtosis and skewness were calculated. Moreover, micro- and macrofossil and sediment geochemical analyses were carried out on six gravity core samples. Study of the above parameters indicates that the anthropogenic impact and intervention are reflected in the micro- (ostracods, foraminifera, charophytes) and macrofossil (molluscs) taxa corresponding to different depositional environmental facies, representing a brackish lagoon with the influence of (a) fresh water inflow, (b) shallow marine environment and (c) hypoxic and dystrophic conditions. The geochemical characteristics and the calculation of the degree of sediment contamination using enrichment factors (EF), contamination factors (Cif) and the index of geo-accumulation (Igeo) indicate a recent relative improvement of the lagoon towards the upper layers of the gravity cores, rendering the lagoon as unpolluted to moderately polluted. This combinatorial study of sediment geochemical characteristics, as well as the downcore micro- and macrofossil assemblages, can be considered as a baseline for future monitoring in accordance with European Union directives, and for any future engineering interventions for the lagoon environmental maintenance and conservation; as this is the first time that geochemical and downcore palaeoecological data have been presented from this lagoon.


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