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This book provides an introduction to the theory and applications of point processes, both in time and in space. Presenting the two components of point process calculus, the martingale calculus and the Palm calculus, it aims to develop the computational skills needed for the study of stochastic models involving point processes, providing enough of the general theory for the reader to reach a technical level sufficient for most applications. Classical and not-so-classical models are examined in detail, including Poisson–Cox, renewal, cluster and branching (Kerstan–Hawkes) point processes.The applications covered in this text (queueing, information theory, stochastic geometry and signal analysis) have been chosen not only for their intrinsic interest but also because they illustrate the theory. Written in a rigorous but not overly abstract style, the book will be accessible to earnest beginners with a basic training in probability but will also interest upper graduate students and experienced researchers.

Probabilities. --- Fourier analysis. --- Probability Theory and Stochastic Processes. --- Fourier Analysis. --- Analysis, Fourier --- Mathematical analysis --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Point processes. --- Processes, Point --- Stochastic processes

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This text offers a mathematically rigorous exposition of the basic theory of marked point processes developing randomly over time, and shows how this theory may be used to treat piecewise deterministic stochastic processes in continuous time. The focus is on point processes that generate only finitely many points in finite time intervals, resulting in piecewise deterministic processes with "few jumps". The point processes are constructed from scratch with detailed proofs and their distributions characterized using compensating measures and martingale structures. Piecewise deterministic processes are defined and identified with certain marked point processes, which are then used in particular to construct and study a large class of piecewise deterministic Markov processes, whether time homogeneous or not. The second part of the book addresses applications of the just developed theory. This analysis of various models in applied statistics and probability includes examples and exercises in survival analysis, branching processes, ruin probabilities, sports (soccer), finance and risk management (arbitrage and portfolio trading strategies), and queueing theory. Graduate students and researchers interested in probabilistic modeling and its applications will find this text an excellent resource, requiring for mastery a solid foundation in probability theory, measure and integration, as well as some knowledge of stochastic processes and martingales. However, an explanatory introduction to each chapter highlights those portions that are crucial and those that can be omitted by non-specialists, making the material more accessible to a wider cross-disciplinary audience.

Point processes. --- Stochastic processes. --- Random processes --- Probabilities --- Processes, Point --- Stochastic processes --- Distribution (Probability theory. --- Mathematics. --- Statistics. --- Mathematical optimization. --- Finance. --- Probability Theory and Stochastic Processes. --- Applications of Mathematics. --- Statistics for Business, Management, Economics, Finance, Insurance. --- Measure and Integration. --- Optimization. --- Quantitative Finance. --- Funding --- Funds --- Economics --- Currency question --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Math --- Science --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities. --- Applied mathematics. --- Engineering mathematics. --- Statistics . --- Measure theory. --- Economics, Mathematical . --- Mathematical economics --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Engineering --- Engineering analysis --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Methodology --- Point processes

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Focusing on the theory and applications of point processes, Point Processes for Reliability Analysis naturally combines classical results on the basic and advanced properties of point processes with recent theoretical findings of the authors. It also presents numerous examples that illustrate how general results and approaches are applied to stochastic description of repairable systems and systems operating in a random environment modelled by shock processes.   The real life objects are operating in a changing, random environment. One of the ways to model an impact of this environment is via the external shocks occurring in accordance with some stochastic point processes. The Poisson (homogeneous and nonhomogeneous) process, the renewal process and their generalizations are considered as models for external shocks affecting an operating system. At the same time these processes model the consecutive failure/repair times of repairable engineering systems. Perfect, minimal and intermediate (imperfect) repairs are discussed in this respect.  Covering material previously available only in the journal literature, Point Processes for Reliability Analysis provides a survey of recent developments in this area which will be invaluable to researchers and advanced students in reliability engineering and applied mathematics.

Point processes. --- Reliability (Engineering) --- Statistical methods. --- Engineering. --- Statistics. --- Engineering economics. --- Engineering economy. --- Manufacturing industries. --- Machines. --- Tools. --- Quality control. --- Reliability. --- Industrial safety. --- Industrial organization. --- Quality Control, Reliability, Safety and Risk. --- Industrial Organization. --- Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences. --- Manufacturing, Machines, Tools. --- Engineering Economics, Organization, Logistics, Marketing. --- Mathematical statistics --- Processes, Point --- Stochastic processes --- System safety. --- Manufactures. --- Manufacturing, Machines, Tools, Processes. --- Economy, Engineering --- Engineering economics --- Industrial engineering --- Manufactured goods --- Manufactured products --- Products --- Products, Manufactured --- Commercial products --- Manufacturing industries --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Industries --- Organization --- Industrial concentration --- Industrial management --- Industrial sociology --- Safety, System --- Safety of systems --- Systems safety --- Accidents --- Industrial safety --- Systems engineering --- Prevention --- Statistics . --- Industrial accidents --- Job safety --- Occupational hazards, Prevention of --- Occupational health and safety --- Occupational safety and health --- Prevention of industrial accidents --- Prevention of occupational hazards --- Safety, Industrial --- Safety engineering --- Safety measures --- Safety of workers --- System safety --- Dependability --- Trustworthiness --- Conduct of life --- Factory management --- Sampling (Statistics) --- Standardization --- Quality assurance --- Quality of products