Distance estimates for dependent thinnings of point processes with densities.
Distance estimates for Poisson process approximations of dependent thinnings.
Doubly stochastic compound Poisson processes in extreme value theory.
Dynamic analysis of a unified multivariate counting process and its asymptotic behavior.
Eigenvalues of GUE minors.
Erratum to “Eigenvalues of GUE minors" [Electron. J. Probab. 11, 1342–1371 (2006; Zbl 1127.60047)].
Espaces de Fock pour les processus de Wiener et de Poisson
Estimation of a Regression Function on a Point Process and its Application to Financial Ruin Risk Forecast
2000 Mathematics Subject Classification: Primary 60G55; secondary 60G25.We estimate a regression function on a point process by the Tukey regressogram method in a general setting and we give an application in the case of a Risk Process. We show among other things that, in classical Poisson model with parameter r, if W is the amount of the claim with finite espectation E(W) = m, Sn (resp. Rn) the accumulated interval waiting time for successive claims (resp. the aggregate claims amount) up to the...
Estimation of reduced Palm distributions by random methods for Cox processes with unknown probability law
Let , i ≥ 1, be i.i.d. observable Cox processes on [a,b] directed by random measures Mi. Assume that the probability law of the Mi is completely unknown. Random techniques are developed (we use data from the processes ,..., to construct a partition of [a,b] whose extremities are random) to estimate L(μ,g) = E(exp(-(N(g) - μ(g))) | N - μ ≥ 0).
Estimation of summary characteristics from replicated spatial point processes
Summary characteristics play an important role in the analysis of spatial point processes. We discuss various approaches to estimating summary characteristics from replicated observations of a stationary point process. The estimators are compared with respect to their integrated squared error. Simulations for three basic types of point processes help to indicate the best way of pooling the subwindow estimators. The most appropriate way depends on the particular summary characteristic, edge-correction...
Estimators of the asymptotic variance of stationary point processes - a comparison
We investigate estimators of the asymptotic variance of a –dimensional stationary point process which can be observed in convex and compact sampling window . Asymptotic variance of is defined by the asymptotic relation (as ) and its existence is guaranteed whenever the corresponding reduced covariance measure has finite total variation. The three estimators discussed in the paper are the kernel estimator, the estimator based on the second order intesity of the point process and the...
Étude de deux évolutions markoviennes de processus ponctuels sur R par des méthodes d'association
Evaluating the bivariate compound generalized Poisson distribution.
Existence and simulation of Gibbs-Delaunay-Laguerre tessellations
Three-dimensional Laguerre tessellation models became quite popular in many areas of physics and biology. They are generated by locally finite configurations of marked points. Randomness is included by assuming that the set of generators is formed by a marked point process. The present paper focuses on 3D marked Gibbs point processes of generators which enable us to specify the desired geometry of the Laguerre tessellation. In order to prove the existence of a stationary Gibbs measure using a general...
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Fine structure of the zeros of orthogonal polynomials. I: A tale of two pictures.
Fractional Poisson processes and related planar random motions.
Functional central limit theorems for seeds in a linear birth and growth model
A problem of heredity of mixing properties (α-mixing, β-mixing and ρ-mixing) from a stationary point process on ℝ × ℝ₊ to a sequence of some of its points called 'seeds' is considered. Next, using the mixing properties, several versions of functional central limit theorems for the distances between seeds and the process of the number of seeds are obtained.
Functionals of spatial point processes having a density with respect to the Poisson process
-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Itô chaos expansion. In the second half we obtain more explicit results for a system of -statistics of some parametric models in stochastic geometry. In the logarithmic form functionals are connected to Gibbs models. There is an inequality between moments of Poisson...
Gaussian approximation for functionals of Gibbs particle processes
In the paper asymptotic properties of functionals of stationary Gibbs particle processes are derived. Two known techniques from the point process theory in the Euclidean space are extended to the space of compact sets on equipped with the Hausdorff metric. First, conditions for the existence of the stationary Gibbs point process with given conditional intensity have been simplified recently. Secondly, the Malliavin-Stein method was applied to the estimation of Wasserstein distance between the...