Appendix A: Mathematical Background
The theory of invariant random fields on spaces with a group action requires good knowledge of various parts of mathematics other than Probability and Statistics. We discuss differentiable manifolds, vector bundles, Lie groups and Lie algebras, group acti
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Editors: S. Asmussen, J. Gani, P. Jagers, T.G. Kurtz
Probability and Its Applications The Probability and Its Applications series publishes research monographs, with the expository quality to make them useful and accessible to advanced students, in probability and stochastic processes, with a particular focus on: – Foundations of probability including stochastic analysis and Markov and other stochastic processes – Applications of probability in analysis – Point processes, random sets, and other spatial models – Branching processes and other models of population growth – Genetics and other stochastic models in biology – Information theory and signal processing – Communication networks – Stochastic models in operations research
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Anatoliy Malyarenko
Invariant Random Fields on Spaces with a Group Action
Anatoliy Malyarenko School of Education, Culture, and Communication Mälardalen University Västerås, Sweden
Series Editors Søren Asmussen Department of Mathematical Sciences Aarhus University Aarhus, Denmark Joe Gani Centre for Mathematics and its Applications Mathematical Sciences Institute Australian National University Canberra, Australia
Peter Jagers Mathematical Statistics Chalmers University of Technology and University of Gothenburg Gothenburg, Sweden Thomas G. Kurtz Department of Mathematics University of Wisconsin–Madison Madison, WI, USA
ISSN 1431-7028 Probability and Its Applications ISBN 978-3-642-33405-4 ISBN 978-3-642-33406-1 (eBook) DOI 10.1007/978-3-642-33406-1 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012952289 Mathematics Subject Classification (2010): 60G60, 60G17, 60G22, 85A40 © Springer-Verlag Berlin Heidelberg 2013 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the
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