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Statistics
A Journal of Theoretical and Applied Statistics
Volume 23, 1992 - Issue 3
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Original Articles

On existence and mixing properties of germ-grain models

L. Heinrich Fachbereich Mathematik, Bergakademie Freiberg, D-O-9200, Freiberg (Sachsen), Germany, Bernhard-von-Cotta-Str. 2
Pages 271-286 | Received 15 May 1991, Accepted 27 Dec 1991, Published online: 27 Jun 2007

Citations (30)

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Read on this site (6)

Christian Bräu & Lothar Heinrich. (2017) Mixing properties of stationary Poisson cylinder models. Stochastics 89:5, pages 753-765.
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Lothar Heinrich & Zbyněk Pawlas. (2008) Weak and strong convergence of empirical distribution functions from germ-grain processes. Statistics 42:1, pages 49-65.
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I.S. Molchanov. (1996) A Limit theorem for scaled vacancies of the boolean model. Stochastics and Stochastic Reports 58:1-2, pages 45-65.
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I. S. Molchanov. (1996) Set-Valued Estimators for Mean Bodies Related to Boolean Models. Statistics 28:1, pages 43-56.
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Lothar Heinrich & Eik Schiile. (1995) Generation of the typical cell of a non-poissonian Johnson-Mehl tessellation. Communications in Statistics. Stochastic Models 11:3, pages 541-560.
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Franz Streit. (1995) Testing Whether Interpenetration is Possible for the Grains of a Random Set. Statistics 26:4, pages 355-364.
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Articles from other publishers (24)

Ian Flint & Nicolas Privault. (2019) Computation of Coverage Probabilities in a Spherical Germ-Grain Model. Methodology and Computing in Applied Probability 23:2, pages 491-502.
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François Willot. 2021. Mechanical Engineering under Uncertainties. Mechanical Engineering under Uncertainties 43 82 .
Lothar Heinrich. (2018) Brillinger-mixing point processes need not to be ergodic. Statistics & Probability Letters 138, pages 31-35.
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Christian Bräu & Lothar Heinrich. (2016) Multivariate Poisson distributions associated with Boolean models. Metrika 79:6, pages 749-761.
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Franz Streit. 2014. Wiley StatsRef: Statistics Reference Online. Wiley StatsRef: Statistics Reference Online.
Jean-François Coeurjolly & Jesper Møller. (2014) Variational approach for spatial point process intensity estimation. Bernoulli 20:3.
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Jean‐Charles Pinoli. 2014. Mathematical Foundations of Image Processing and Analysis 2. Mathematical Foundations of Image Processing and Analysis 2 349 433 .
Jean‐Charles Pinoli. 2014. Mathematical Foundations of Image Processing and Analysis 1. Mathematical Foundations of Image Processing and Analysis 1 309 392 .
. 2013. Stochastic Geometry and its Applications. Stochastic Geometry and its Applications 453 505 .
Lothar Heinrich. 2013. Stochastic Geometry, Spatial Statistics and Random Fields. Stochastic Geometry, Spatial Statistics and Random Fields 115 150 .
R. Lachièze-Rey. (2016) Mixing properties for STIT tessellations. Advances in Applied Probability 43:1, pages 40-48.
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URSA PANTLE, VOLKER SCHMIDT & EVGENY SPODAREV. (2010) On the Estimation of Integrated Covariance Functions of Stationary Random Fields. Scandinavian Journal of Statistics 37:1, pages 47-66.
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L. Heinrich & M. Spiess. (2009) Berry–Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes. Lithuanian Mathematical Journal 49:4, pages 381-398.
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Franz Streit. 2004. Encyclopedia of Statistical Sciences. Encyclopedia of Statistical Sciences.
Volker Schmidt & Evgueni Spodarev. (2005) Joint estimators for the specific intrinsic volumes of stationary random sets. Stochastic Processes and their Applications 115:6, pages 959-981.
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Lothar Heinrich. (2005) Large deviations of the empirical volume fraction for stationary Poisson grain models. The Annals of Applied Probability 15:1A.
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Dietrich Stoyan & Klaus Mecke. 2005. Space, Structure and Randomness. Space, Structure and Randomness 151 181 .
Franz Streit. 2004. Encyclopedia of Statistical Sciences. Encyclopedia of Statistical Sciences.
Daniel Hug, Günter Last & Wolfgang Weil. 2002. Morphology of Condensed Matter. Morphology of Condensed Matter 317 357 .
Daniel Hug & Günter Last. (2000) On support measures in Minkowski spaces and contact distributions in stochastic geometry. The Annals of Probability 28:2.
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Lothar Heinrich & Ilya S. Molchanov. (2016) Central limit theorem for a class of random measures associated with germ-grain models. Advances in Applied Probability 31:2, pages 283-314.
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Dietrich Stoyan. (2007) Random Sets: Models and Statistics. International Statistical Review 66:1, pages 1-27.
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L. Heinrich & I. S. Molchanov. (2006) Some Limit Theorems for Extremal and Union Shot‐Noise Processes. Mathematische Nachrichten 168:1, pages 139-159.
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Lothar Heinrich. (1993) Asymptotic properties of minimum contrast estimators for parameters of boolean models. Metrika 40:1, pages 67-94.
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