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Introductory Lectures on Fluctuations of Lévy Processes with Applications
Lévy processes are the natural continuous-time analogue of random walks and form a rich class of stochastic processes around which a robust mathematical theory exists. Their mathematical significance is justified by their application in many areas of classical and modern stochastic models including storage models, renewal processes, insurance risk models, optimal stopping problems, mathematical finance and continuous-state branching processes.The book aims to be mathematically rigorous while still providing an intuitive feel for underlying principles. The results and applications often focus on the case of Lévy processes with jumps in only one direction.
Interacting Stochastic Systems
The Research Network on "Interacting stochastic systems of high complexity" set up by the German Research Foundation aimed at exploring and developing connections between research in infinite-dimensional stochastic analysis, statistical physics, spatial population models from mathematical biology, complex models of financial markets or of stochastic models interacting with other sciences. This book presents a structured collection of papers on the core topics, written at the close of the 6-year programme by the research groups who took part in it. The structure chosen highlights the interweaving of certain themes and certain interconnections discovered through the joint work.
Lagrangian Probability Distributions
Lagrangian expansions can be used to obtain numerous useful probability models, which have been applied to real life situations including, but not limited to: branching processes, queuing processes, stochastic processes, environmental toxicology, diffusion of information, ecology, strikes in industries, sales of new products, and production targets for optimum profits. This book presents a comprehensive, systematic treatment of the class of Lagrangian probability distributions, along with some of its families, their properties, and important applications.
Case Studies in Spatial Point Process Modeling
Point process statistics is successfully used in fields such as material science, human epidemiology, social sciences, animal epidemiology, biology, and seismology. Its further application depends greatly on good software and instructive case studies that show the way to successful work. This book satisfies this need by a presentation of the spatstat package and many statistical examples.Researchers, spatial statisticians and scientists from biology, geosciences, materials sciences and other fields will use this book as a helpful guide to the application of point process statistics. No other book presents so many well-founded point process case studies.
