Random Mosaics

By a mosaic we understand a system of convex polytopes in R d that cover the whole space and have pairwise no common interior points. A random mosaic can alternatively be described as a special random closed set (formed by the boundaries of the cells of t

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Editors: J. Gani, C.C. Heyde, P. Jagers, T.G. Kurtz

Probability and Its Applications Azencott et al.: Series of Irregular Observations. Forecasting and Model Building. 1986 Bass: Diffusions and Elliptic Operators. 1997 Bass: Probabilistic Techniques in Analysis. 1995 Berglund/Gentz: Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach. 2006 Biagini/Hu/Øksendal/Zhang: Stochastic Calculus for Fractional Brownian Motion and Applications. 2008 Chen: Eigenvalues, Inequalities and Ergodic Theory. 2005 Costa/Fragoso/Marques: Discrete-Time Markov Jump Linear Systems. 2005 Daley/Vere-Jones: An Introduction to the Theory of Point Processes I: Elementary Theory and Methods. 2nd ed. 2003, corr. 2nd printing 2005 Daley/Vere-Jones: An Introduction to the Theory of Point Processes II: General Theory and Structure. 2nd ed. 2008 de la Peña/Gine: Decoupling: From Dependence to Independence, Randomly Stopped Processes, U-Statistics and Processes, Martingales and Beyond. 1999 Del Moral: Feynman-Kac Formulae. Genealogical and Interacting Particle Systems with Applications. 2004 Durrett: Probability Models for DNA Sequence Evolution. 2002, 2nd ed. 2008 Galambos/Simonelli: Bonferroni-Type Inequalities with Equations. 1996 Gani (ed.): The Craft of Probabilistic Modelling. A Collection of Personal Accounts. 1986 Gut: Stopped Random Walks. Limit Theorems and Applications. 1987 Guyon: Random Fields on a Network. Modeling, Statistics and Applications. 1995 Kallenberg: Foundations of Modern Probability. 1997, 2nd ed. 2002 Kallenberg: Probabilistic Symmetries and Invariance Principles. 2005 Last/Brandt: Marked Point Processes on the Real Line. 1995 Molchanov: Theory of Random Sets. 2005 Nualart: The Malliavin Calculus and Related Topics, 1995, 2nd ed. 2006 Rachev/Rueschendorf: Mass Transportation Problems. Volume I: Theory and Volume II: Applications. 1998 Resnick: Extreme Values, Regular Variation and Point Processes. 1987 Schmidli: Stochastic Control in Insurance. 2008 Schneider/Weil: Stochastic and Integral Geometry. 2008 Shedler: Regeneration and Networks of Queues. 1986 Silvestrov: Limit Theorems for Randomly Stopped Stochastic Processes. 2004 Thorisson: Coupling, Stationarity and Regeneration. 2000

Rolf Schneider · Wolfgang Weil

Stochastic and Integral Geometry

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Rolf Schneider

Wolfgang Weil

Mathematisches Institut Albert-Ludwigs-Universität Eckerstr. 1 79104 Freiburg Germany [email protected]

Institut für Algebra und Geometrie Universität Karlsruhe Englerstraße 2 76128 Karlsruhe Germany [email protected]

Series Editors: Joe Gani Chris Heyde

Thomas G. Kurtz

Centre for Mathematics and its Applications Mathematical Sciences Institute Australian National University Canberra, ACT 0200 Australia [email protected]

Department of Mathematics University of Wisconsin - Madison 480 Lincoln Drive Madison, WI 53706-1388 USA [email protected]

Peter Jagers Mathematical Statistics Chalmers University of Technology and Göteborg (Gothenburg) University 412 96 Göteborg Sweden jagers@chalmer