Facts from Convex Geometry
In this book, the more concrete examples of random sets are generated as unions of random systems of convex bodies. The quantitative description of such random sets is based on functionals of convex bodies which are particularly adapted to taking unions:
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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
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