Complex stochastic systems comprises a vast area of research, from modelling specific applications to model fitting, estimation procedures, and computing issues. The exponential growth in computing power over the last two decades has revolutionized statistical analysis and led to rapid developments and great progress in this emerging field. In Complex Stochastic Systems, leading researchers address various statistical aspects of the field, illustrated by some very concrete applications. A Primer on Markov Chain Monte Carlo by Peter J. Green provides a wide-ranging mixture of the mathematical and statistical ideas, enriched with concrete examples and more than 100 references. Causal Inference from Graphical Models by Steffen L. Lauritzen explores causal concepts in connection with modelling complex stochastic systems, with focus on the effect of interventions in a given system. State Space and Hidden Markov Models by Hans R. Kunschshows the variety of applications of this concept to time series in engineering, biology, finance, and geophysics. Monte Carlo Methods on Genetic Structures by Elizabeth A. Thompson investigates special complex systems and gives a concise introduction to the relevant biological methodology. Renormalization of Interacting Diffusions by Frank den Hollander presents recent results on the large space-time behavior of infinite systems of interacting diffusions. Stein's Method for Epidemic Processes by Gesine Reinert investigates the mean field behavior of a general stochastic epidemic with explicit bounds. Individually, these articles provide authoritative, tutorial-style exposition and recent results from various subjects related to complex stochastic systems. Collectively, they link these separate areas of study to form the first comprehensive overview of this rapidly developing field.

Complex stochastic systems comprises a vast area of research, from modelling specific applications to model fitting, estimation procedures, and computing issues. The exponential growth in computing power over the last two decades has revolutionized statistical analysis and led to rapid developments and great progress in this emerging field. In Complex Stochastic Systems, leading researchers address various statistical aspects of the field, illustrated by some very concrete applications.

A Primer on Markov Chain Monte Carlo by Peter J. Green provides a wide-ranging mixture of the mathematical and statistical ideas, enriched with concrete examples and more than 100 references.
Causal Inference from Graphical Models by Steffen L. Lauritzen explores causal concepts in connection with modelling complex stochastic systems, with focus on the effect of interventions in a given system.
State Space and Hidden Markov Models by Hans R. Künschshows the variety of applications of this concept to time series in engineering, biology, finance, and geophysics.
Monte Carlo Methods on Genetic Structures by Elizabeth A. Thompson investigates special complex systems and gives a concise introduction to the relevant biological methodology.
Renormalization of Interacting Diffusions by Frank den Hollander presents recent results on the large space-time behavior of infinite systems of interacting diffusions.
Stein's Method for Epidemic Processes by Gesine Reinert investigates the mean field behavior of a general stochastic epidemic with explicit bounds.

Individually, these articles provide authoritative, tutorial-style exposition and recent results from various subjects related to complex stochastic systems. Collectively, they link these separate areas of study to form the first comprehensive overview of this rapidly developing field.

This is a unique book addressing the integration of risk methodology from various fields. It will stimulate intellectual debate and communication across disciplines, promote better risk management practices and contribute to the development of risk management methodologies. Individual chapters explain fundamental risk models and measurement, and address risk and security issues from diverse areas such as finance and insurance, the health sciences, life sciences, engineering and information science. Integrated Risk Sciences is an emerging discipline that considers risks in different fields, aiming at a common language, and at sharing and improving methods developed in different fields. Readers should have a Bachelor degree and have taken at least one basic university course in statistics and probability. The main goal of the book is to provide basic knowledge on risk and security in a common language; the authors have taken particular care to ensure that all content can readily be understood by doctoral students and researchers across disciplines. Each chapter provides simple case studies and examples, open research questions and discussion points, and a selected bibliography inviting readers to further study.

Both in insurance and in finance applications, questions involving extremal events (such as large insurance claims, large fluctuations in financial data, stock market shocks, risk management, ...) play an increasingly important role. This book sets out to bridge the gap between the existing theory and practical applications both from a probabilistic as well as from a statistical point of view. Whatever new theory is presented is always motivated by relevant real-life examples. The numerous illustrations and examples, and the extensive bibliography make this book an ideal reference text for students, teachers and users in the industry of extremal event methodology.

Over the past 10-15 years, we have seen a revival of general Levy ' processes theory as well as a burst of new applications. In the past, Brownian motion or the Poisson process have been considered as appropriate models for most applications. Nowadays, the need for more realistic modelling of irregular behaviour of phen- ena in nature and society like jumps, bursts, and extremeshas led to a renaissance of the theory of general Levy ' processes. Theoretical and applied researchers in elds asdiverseas quantumtheory,statistical physics,meteorology,seismology,statistics, insurance, nance, and telecommunication have realised the enormous exibility of Lev ' y models in modelling jumps, tails, dependence and sample path behaviour. L' evy processes or Levy ' driven processes feature slow or rapid structural breaks, extremal behaviour, clustering, and clumping of points. Toolsandtechniquesfromrelatedbut disctinct mathematical elds, such as point processes, stochastic integration,probability theory in abstract spaces, and differ- tial geometry, have contributed to a better understanding of Le 'vy jump processes. As in many other elds, the enormous power of modern computers has also changed the view of Levy ' processes. Simulation methods for paths of Levy ' p- cesses and realisations of their functionals have been developed. Monte Carlo simulation makes it possible to determine the distribution of functionals of sample paths of Levy ' processes to a high level of accuracy.