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The transport of neutrons in a multiplying system is an area of branching processes with a clear formalism. This book presents an account of the mathematical tools used in describing branching processes, which are then used to derive a large number of properties of the neutron distribution in multiplying systems with or without an external source. In the second part of the book, the theory is applied to the description of the neutron fluctuations in nuclear reactor cores as well as in small samples of fissile material. The question of how to extract information about the system under s

Branching processes. --- Neutrons. --- Atoms --- Baryons --- Matter --- Particles (Nuclear physics) --- Processes, Branching --- Stochastic processes --- Constitution

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The book presents an overview and brief description of the most frequent methods of phylogenetic inference. It provides basic information on underlying assumptions of these methods, their advantages and disadvantages, and differences between them. The text is supposed to help readers to make informed decisions in choosing an optimal approach for solving a given problem and for a given type of data as well as in correct interpretation of results. The book begins with an overview of the types of data for phylogenetic analysis, databases and sequence alignment, followed by methods of parsimony, evolutionary models, distance methods, likelihood, Bayesian inference, testing hypotheses, and comparing phylogenies. A separate chapter is focused on phylogenetic methods based on morphological data. The final part deals with the theory of coalescent which is essential for an array of population genetic analyses including new approaches to phylogeography.

Cladistic analysis. --- Cladistic analysis --- Cladism --- Cladistic method --- Cladistic taxonomy --- Cladistics --- Cladograms --- Phylogenetic systematics --- Phylogenetic taxonomy --- Taxonomy, Cladistic --- Taxonomy, Phylogenetic --- Biology --- Branching processes --- Phylogeny --- Data processing. --- Classification

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This unique volume discusses some recent developments in the theory of spatial branching processes and superprocesses, with special emphasis on spines, laws of large lumbers, interactions and random media. Although this book is mainly written for mathematicians, the models discussed are relevant to certain models in population biology, and are thus hopefully interesting to the applied mathematician/biologist as well. The necessary background material in probability and analysis is provided in a comprehensive introductory chapter. Historical notes and several exercises are provided to complement each chapter.

Mathematical statistics. --- Branching processes. --- Law of large numbers. --- Large numbers, Law of --- Numbers, Large --- Convergence --- Mathematical statistics --- Probabilities --- Processes, Branching --- Stochastic processes --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Sampling (Statistics) --- Statistical methods

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This is the first volume of a subseries of the Lecture Notes in Mathematics which will appear randomly over the next years. Each volume will describe some important topic in the theory or applications of Lévy processes and pay tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. The three expository articles of this first volume have been chosen to reflect the breadth of the area of Lévy processes. The first article by Ken-iti Sato characterizes extensions of the class of selfdecomposable distributions on R^d. The second article by Thomas Duquesne discusses Hausdorff and packing measures of stable trees. The third article by Oleg Reichmann and Christoph Schwab presents numerical solutions to Kolmogoroff equations, which arise for instance in financial engineering, when Lévy or additive processes model the dynamics of the risky assets.

Lâevy processes --- Branching processes --- Trees (Graph theory) --- Options (Finance) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Prices --- Mathematical models --- Branching processes. --- Lévy processes. --- Lévy, Paul, --- Processes, Branching --- Mathematics. --- Probabilities. --- Probability Theory and Stochastic Processes. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Math --- Science --- Graph theory --- Random walks (Mathematics) --- Stochastic processes --- Distribution (Probability theory. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Levy processes. --- Levy, Paul,

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This volume is dedicated to the memory of the late Professor C.C. (Chris) Heyde (1939-2008), distinguished statistician, mathematician and scientist. Chris worked at a time when many of the foundational building blocks of probability and statistics were being put in place by a phalanx of eminent scientists around the world. He contributed significantly to this effort and took his place deservedly among the top-most rank of researchers. Throughout his career, Chris maintained also a keen interest in applications of probability and statistics, and in the history of the subject. The magnitude of his impact on his chosen area of research, both in Australia and internationally, was well recognised by the abundance of honours he received within and without the profession. The book is comprised of a number of Chris’s papers covering each one of four major topics to which he contributed. These papers are reproduced herein. The topics, and the papers in them, were selected by four of Chris’s friends and collaborators: Ishwar Basawa, Peter Hall, Ross Maller (overall Editor of the volume) and Eugene Seneta. Each topic is provided with an overview by the selecting editor. The topics cover a range of areas to which Chris made especially important contributions: Inference in Stochastic Processes, Rates of Convergence in the Central Limit Theorem, the Law of the Iterated Logarithm, and Branching Processes and Population Genetics. The Editor and the other contributors to the volume include well known researchers in probability and statistics. The collection begins with an “author’s pick” of a number of his papers which Chris considered most interesting and significant, chosen by him shortly before his death. A biography of Chris by his close friend and collaborator, Joe Gani, is also included. An introduction by the Editor and a comprehensive bibliography of Chris’s publications complete the volume. The book will be of especial interest to researchers in probability and statistics, and in the history of these subjects.

Branching processes. --- Limit theorems (Probability theory). --- Mathematical statistics. --- Probabilities. --- Stochastic processes. --- Mathematical statistics --- Probabilities --- Stochastic processes --- Branching processes --- Limit theorems (Probability theory) --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Statistics --- Random processes --- Probability --- Statistical inference --- Statistics. --- Economics, Mathematical. --- Biomathematics. --- Econometrics. --- Statistical Theory and Methods. --- Probability Theory and Stochastic Processes. --- Mathematical and Computational Biology. --- Quantitative Finance. --- Combinations --- Chance --- Least squares --- Risk --- Distribution (Probability theory. --- Finance. --- Funding --- Funds --- Economics --- Currency question --- Economics, Mathematical --- Statistics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Statistics, Mathematical --- Sampling (Statistics) --- Statistical methods --- Statistics . --- Economics, Mathematical . --- Mathematical economics --- Econometrics --- Biology --- Statistical analysis --- Statistical data --- Statistical science --- Methodology