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Extremes and Related Properties of Random Sequences and Processes
Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued.
Mass Transportation Problems
The first comprehensive account of the theory of mass transportation problems and its applications. In Volume I, the authors systematically develop the theory with emphasis on the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment problems. They then discuss a variety of different approaches towards solving these problems and exploit the rich interrelations to several mathematical sciences - from functional analysis to probability theory and mathematical economics. The second volume is devoted to applications of the above problems to topics in applied probability, theory of moments and distributions with given marginals, queuing theory, risk theory of probability metrics and its applications to various fields, among them general limit theorems for Gaussian and non-Gaussian limiting laws, stochastic differential equations and algorithms, and rounding problems. Useful to graduates and researchers in theoretical and applied probability, operations research, computer science, and mathematical economics, the prerequisites for this book are graduate level probability theory and real and functional analysis.
Weak Convergence of Financial Markets
A comprehensive overview of weak convergence of stochastic processes and its application to the study of financial markets. Split into three parts, the first recalls the mathematics of stochastic processes and stochastic calculus with special emphasis on contiguity properties and weak convergence of stochastic integrals. The second part is devoted to the analysis of financial theory from the convergence point of view. The main problems, which include portfolio optimization, option pricing and hedging are examined, especially when considering discrete-time approximations of continuous-time dynamics. The third part deals with lattice- and tree-based computational procedures for option pricing both on stocks and stochastic bonds. More general discrete approximations are also introduced and detailed. Includes detailed examples.
Mathematical And Statistical Methods In Reliability
This book contains extended versions of 34 carefully selected and reviewed papers presented at the Third International Conference on Mathematical Methods in Reliability, held in Trondheim, Norway in 2002. It provides a broad overview of current research activities in reliability theory and its applications. There are chapters on reliability modelling, network and system reliability, reliability optimization, survival analysis, degradation and maintenance modelling, and software reliability. The authors are all leading experts in the field.A particular feature of the book is a historical review by Professor Richard E Barlow, well known for his pioneering research on reliability. The list of authors also includes the plenary session speakers Odd O Aalen, Philip J Boland, Sallie A Keller-McNulty, and Nozer Singpurwalla.
Risk Budgeting
Institutionelle Anleger, Fonds- und Portfoliomanager müssen Risiken eingehen, wenn sie Spitzengewinne erzielen wollen. Die Frage ist nur wieviel Risiko. "Risk Budgeting: Portfolio Problem Solving with VaR" liefert die Antwort auf diese Frage. Beim Konzept des Risk Budgeting geht es um Risiko- und Kapitalallokation auf der Grundlage erwarteter Erträge und Risiken, mit dem Ziel, höhere Renditen zu erwirtschaften im Rahmen eines vordefinierten Gesamtrisikoniveaus. Mit Hilfe quantitativer Methoden zur Risikomessung, einschließlich der Value at Risk-Methode läßt sich das Risiko ermitteln und bewerten. Value at Risk (VaR) ist ein Verfahren zur Risikobewertung, das Banken ursprünglich zur Me...
Genetics of Adaptation
An enduring controversy in evolutionary biology is the genetic basis of adaptation. Darwin emphasized "many slight differences" as the ultimate source of variation to be acted upon by natural selection. In the early 1900’s, this view was opposed by "Mendelian geneticists", who emphasized the importance of "macromutations" in evolution. The Modern Synthesis resolved this controversy, concluding that mutations in genes of very small effect were responsible for adaptive evolution. A decade ago, Allen Orr and Jerry Coyne reexamined the evidence for this neo-Darwinian view and found that both the theoretical and empirical basis for it were weak. Orr and Coyne encouraged evolutionary biologists to reexamine this neglected question: what is the genetic basis of adaptive evolution? In this volume, a new generation of biologists have taken up this challenge. Using advances in both molecular genetic and statistical techniques, evolutionary geneticists have made considerable progress in this emerging field. In this volume, a diversity of examples from plant and animal studies provides valuable information for those interested in the genetics and evolution of complex traits.
Robust Control of Linear Systems and Nonlinear Control
This volume is the second of the three volume publication containing the proceedings of the 1989 International Symposium on the Mathemat ical Theory of Networks and Systems (MTNS-89), which was held in Amsterdam, The Netherlands, June 19-23, 1989 The International Symposia MTNS focus attention on problems from system and control theory, circuit theory and signal processing, which, in general, require application of sophisticated mathematical tools, such as from function and operator theory, linear algebra and matrix theory, differential and algebraic geometry. The interaction between advanced mathematical methods and practical engineering problems of circuits, systems and control, which is t...
Extreme Events
The monograph covers the fundamentals and the consequences of extreme geophysical phenomena like asteroid impacts, climatic change, earthquakes, tsunamis, hurricanes, landslides, volcanic eruptions, flooding, and space weather. This monograph also addresses their associated, local and worldwide socio-economic impacts. The understanding and modeling of these phenomena is critical to the development of timely worldwide strategies for the prediction of natural and anthropogenic extreme events, in order to mitigate their adverse consequences. This monograph is unique in as much as it is dedicated to recent theoretical, numerical and empirical developments that aim to improve: (i) the understandi...
Foundations Of Complex Systems: Emergence, Information And Prediction (2nd Edition)
This book provides a self-contained presentation of the physical and mathematical laws governing complex systems. Complex systems arising in natural, engineering, environmental, life and social sciences are approached from a unifying point of view using an array of methodologies such as microscopic and macroscopic level formulations, deterministic and probabilistic tools, modeling and simulation. The book can be used as a textbook by graduate students, researchers and teachers in science, as well as non-experts who wish to have an overview of one of the most open, markedly interdisciplinary and fast-growing branches of present-day science.
