Branching Processes

The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has developed and matured significan

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llerausgegeben von

J. L. Doob . A. Grothendieck . E. Heinz· F. Hirzebruch E. Hopf . W Maak . S. Mac Lane· W Magnus· J. K. Moser M. M. Postnikov . F. K. Schmidt· D. S. Scott· K. Stein

Geschaftsfiihrende IIerausgeber

B. Eckmann und B. L. van der Waerden

K. B. Athreya . P. E. Ney

Branching Processes

Springer-Verlag Berlin Heidelberg New York 1972

Krishna B. Athreya Associate Professor of Mathematics University of Wisconsin, Madison, Wisconsin

Peter E. Ney Professor of Mathematics University of Wisconsin, Madison, Wisconsin

Geschaftsfiihrende Herausgeber:

B. Eckmann Eidgeniissische Technische Hochschule Ziirich

B. L. van der Waerden Mathematisches Institut der Universitiit Ziirich

AMS Subject Classifications (1970) Primary 60J80, 60K99, 60F99 Secondary 60J85, 39A20, 45M05, 60J 45, 92A 15

ISBN -13: 978- 3-642-65373-5 e- ISBN -13: 978-3-642-65371-1 DOl: 10.1007/978-3-642-65371-1

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data qanks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by SpringerVerlag Berlin Heidelberg 1972. Library of Congress Catalog Card Number 72-75819. Softcover reprint of the hardcover 1st edition 1972

K. B. Athreya . P. E. Ney

Branching Processes

Springer-Verlag New York Heidelberg Berlin 1972

Krishna B. Athreya Associate Professor of Mathematics University of Wisconsin, Madison, Wisconsin

Peter E. Ney Professor of Mathematics

University of Wisconsin, Madison, Wisconsin

Geschliftsfiihrende Herausgeber:

B. Eckmann Eidgeniissische Technische Hochschule Ziirich

B. L. van der Waerden Mathematisches Institut der Universit.t Ziirich

AMS Subject Classifications (1970) Primary 60 J 80, 60 K 99, 60 F 99 Secondary 60J 85, 39A20, 45 M05, 60J 45, 92A 15

ISBN -13: 978-3-642-65373-5 e- ISBN -13: 978-3-642-65371-1 DOl: 10.1007/978-3-642-65371-1

This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data hanks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by SpringerVerlag Berlin Heidelberg 1972. Library of Congress Catalog Card Number 72-75819. Softcover reprint of the hardcover 1st edition 1972

Dedicated to our parents

Preface The purpose of this book is to give a unified treatment of the limit theory of branching processes. Since the publication of the important book of T E. Harris (Theory of Branching Processes, Springer, 1963) the subject has d