Handbook of Probability

Ionut Florescu 지음

Wiley 2013년 10월 28일 출간

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THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITYWritten in a clear, accessible, and comprehensive manner, the Handbook of Probability presents the fundamentals of probability with an emphasis on the balance of theory, application, and methodology. Utilizing basic examples throughout, the handbook expertly transitions between concepts and practice to allow readers an inclusive introduction to the field of probability.The book provides a useful format with self-contained chapters, allowing the reader easy and quick reference. Each chapter includes an introduction, historical background, theory and applications, algorithms, and exercises. The Handbook of Probability offers coverage of:Probability SpaceProbability MeasureRandom VariablesRandom Vectors in RnCharacteristic FunctionMoment Generating FunctionGaussian Random VectorsConvergence TypesLimit TheoremsThe Handbook of Probability is an ideal resource for researchers and practitioners in numerous fields, such as mathematics, statistics, operations research, engineering, medicine, and finance, as well as a useful text for graduate students.

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List of Figures xvList of Tables xviiPreface xixIntroduction xxi1 Probability Space 11.1 Introduction/Purpose of the Chapter 11.2 Vignette/Historical Notes 21.3 Notations and Definitions 31.4 Theory and Applications 4Problems 122 Probability Measure 152.1 Introduction/ Purpose of the chapter 152.2 Vignette/ Historical Notes 162.3 Theory and Applications 172.4 Examples 232.5 Monotone Convergence properties of probability 252.6 Conditional Probability 272.7 Independence of events and sigma fields 352.8 Borel Cantelli Lemmas 412.9 The Fatou lemmas 432.10 Kolmogorov zeroone law 442.11 Lebesgue measure on the unit interval (0,1] 45Problems 483 Random Variables: Generalities 593.1 Introduction/ Purpose of the chapter 593.2 Vignette/Historical Notes 593.3 Theory and Applications 603.4 Independence of random variables 66Problems 674 Random Variables: the discrete case 754.1 Introduction/Purpose of the chapter 754.2 Vignette/Historical Notes 764.3 Theory and Applications 764.4 Examples of discrete random variables 84Problems 1025 Random Variables: the continuous case 1135.1 Introduction/purpose of the chapter 1135.2 Vignette/Historical Notes 1145.3 Theory and Applications 1145.4 Moments 1195.5 Change of variables 1205.6 Examples 1216 Generating Random variables 1616.1 Introduction/Purpose of the chapter 1616.2 Vignette/Historical Notes 1626.3 Theory and applications 1626.4 Generating multivariate distributions with prescribed covariance structure 188Problems 1917 Random vectors in Rn 1937.1 Introduction/Purpose of the chapter 1937.2 Vignette/Historical Notes 1

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저자(글) Ionut Florescu

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IONUT FLORESCU, PhD, is Research Associate Professor of Financial Engineering and Director of the Hanlon Financial Systems Lab at Stevens Institute of Technology. He has published extensively in his areas of research interest, which include stochastic volatility, stochastic partial differential equations, Monte Carlo methods, and numerical methods for stochastic processes.CIPRIAN A. TUDOR, PhD, is Professor of Mathematics at the University of Lille 1, France. His research interests include Brownian motion, limit theorems, statistical inference for stochastic processes, and financial mathematics. He has over eighty scientific publications in various internationally recognized journals on probability theory and statistics. He serves as a referee for over a dozen journals and has spoken at more than thirty#45;five conferences worldwide.