The Nile on eBay FREE SHIPPING UK WIDE Handbook of Probability by Ionut Florescu, Ciprian A. Tudor
This handbook provides a complete, but accessible compendium of all the major theorems, applications, and methodologies that are necessary for a clear understanding of probability. Each chapter is self-contained utilizing a common format. Algorithms and formulae are stressed when necessary and in an easy-to-locate fashion.
FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description
THE COMPLETE COLLECTION NECESSARY FOR A CONCRETE UNDERSTANDING OF PROBABILITY Written 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 Space Probability MeasureRandom VariablesRandom Vectors in RnCharacteristic FunctionMoment Generating FunctionGaussian Random VectorsConvergence TypesLimit Theorems The 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.
Back Cover
The complete collection necessary for A CONCRETE understanding of probability Written 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 Space Random Variables Characteristic Function Gaussian Random Vectors Limit Theorems Probability Measure Random Vectors in Rn Moment Generating Function Convergence Types The 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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The complete collection necessary for A CONCRETE understanding of probability Written 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 Space Random Variables Characteristic Function Gaussian Random Vectors Limit Theorems Probability Measure Random Vectors in Rn Moment Generating Function Convergence Types The 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.
Author Biography
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-five conferences worldwide.
Table of Contents
List of Figures xvPreface xviiIntroduction xix1 Probability Space 11.1 Introduction/Purpose of the Chapter 11.2 Vignette/Historical Notes 21.3 Notations and Definitions 21.4 Theory and Applications 41.4.1 Algebras 41.4.2 Sigma Algebras 51.4.3 Measurable Spaces 71.4.4 Examples 71.4.5 The Borel _-Algebra 91.5 Summary 12Exercises 122 Probability Measure 152.1 Introduction/Purpose of the Chapter 152.2 Vignette/Historical Notes 162.3 Theory and Applications 172.3.1 Definition and Basic Properties 172.3.2 Uniqueness of Probability Measures 222.3.3 Monotone Class 242.3.4 Examples 262.3.5 Monotone Convergence Properties of Probability 282.3.6 Conditional Probability 312.3.7 Independence of Events and _-Fields 392.3.8 Borel–Cantelli Lemmas 462.3.9 Fatou's Lemmas 482.3.10 Kolmogorov's Zero–One Law 492.4 Lebesgue Measure on the Unit Interval (01] 50Exercises 523 Random Variables: Generalities 633.1 Introduction/Purpose of the Chapter 633.2 Vignette/Historical Notes 633.3 Theory and Applications 643.3.1 Definition 643.3.2 The Distribution of a Random Variable 653.3.3 The Cumulative Distribution Function of a Random Variable 673.3.4 Independence of Random Variables 70Exercises 714 Random Variables: The Discrete Case 794.1 Introduction/Purpose of the Chapter 794.2 Vignette/Historical Notes 804.3 Theory and Applications 804.3.1 Definition and Basic Facts 804.3.2 Moments 844.4 Examples of Discrete Random Variables 894.4.1 The (Discrete) Uniform Distribution 894.4.2 Bernoulli Distribution 914.4.3 Binomial (n p) Distribution 924.4.4 Geometric (p) Distribution 954.4.5 Negative Binomial (r p) Distribution 1014.4.6 Hypergeometric Distribution (N m n) 1024.4.7 Poisson Distribution 104Exercises 1085 Random Variables: The Continuous Case 1195.1 Introduction/Purpose of the Chapter 1195.2 Vignette/Historical Notes 1195.3 Theory and Applications 1205.3.1 Probability Density Function (p.d.f.) 1205.3.2 Cumulative Distribution Function (c.d.f.) 1245.3.3 Moments 1275.3.4 Distribution of a Function of the Random Variable 1285.4 Examples 1305.4.1 Uniform Distribution on an Interval [ab] 1305.4.2 Exponential Distribution 1335.4.3 Normal Distribution (_ _2) 1365.4.4 Gamma Distribution 1395.4.5 Beta Distribution 1445.4.6 Student's t Distribution 1475.4.7 Pareto Distribution 1495.4.8 The Log-Normal Distribution 1515.4.9 Laplace Distribution 1535.4.10 Double Exponential Distribution 155Exercises 1566 Generating Random Variables 1776.1 Introduction/Purpose of the Chapter 1776.2 Vignette/Historical Notes 1786.3 Theory and Applications 1786.3.1 Generating One-Dimensional Random Variables by Inverting the Cumulative Distribution Function (c.d.f.) 1786.3.2 Generating One-Dimensional Normal Random Variables 1836.3.3 Generating Random Variables. Rejection Sampling Method 1866.3.4 Generating from a Mixture of Distributions 1936.3.5 Generating Random Variables. Importance Sampling 1956.3.6 Applying Importance Sampling 1986.3.7 Practical Consideration: Normalizing Distributions 2016.3.8 Sampling Importance Resampling 2036.3.9 Adaptive Importance Sampling 2046.4 Generating Multivariate Distributions with Prescribed Covariance Structure 205Exercises 2087 Random Vectors in Rn 2107.1 Introduction/Purpose of the Chapter 2107.2 Vignette/Historical Notes 2107.3 Theory and Applications 2117.3.1 The Basics 2117.3.2 Marginal Distributions 2127.3.3 Discrete Random Vectors 2147.3.4 Multinomial Distribution 2197.3.5 Testing Whether Counts are Coming from a Specific Multinomial Distribution 2207.3.6 Independence 2217.3.7 Continuous Random Vectors 2237.3.8 Change of Variables. Obtaining Densities of Functions of Random Vectors 2297.3.9 Distribution of Sums of Random Variables. Convolutions 231Exercises 2368 Characteristic Function 2558.1 Introduction/Purpose of the Chapter 2558.2 Vignette/Historical Notes 2558.3 Theory and Applications 2568.3.1 Definition and Basic Properties 2568.3.2 The Relationship Between the Characteristic Function and the Distribution 2608.4 Calculation of the Characteristic Function for Commonly Encountered Distributions 2658.4.1 Bernoulli and Binomial 2658.4.2 Uniform Distribution 2668.4.3 Normal Distribution 2678.4.4 Poisson Distribution 2678.4.5 Gamma Distribution 2688.4.6 Cauchy Distribution 2698.4.7 Laplace Distribution 2708.4.8 Stable Distributions. L´evy Distribution 2718.4.9 Truncated L´evy Flight Distribution 274Exercises 2759 Moment-Generating Function 2809.1 Introduction/Purpose of the Chapter 2809.2 Vignette/Historical Notes 2809.3 Theory and Applications 2819.3.1 Generating Functions and Applications 2819.3.2 Moment-Generating Functions. Relation with the Characteristic Functions 2889.3.3 Relationship with the Characteristic Function 2929.3.4 Properties of the MGF 292Exercises 29410 Gaussian Random Vectors 30010.1 Introduction/Purpose of the Chapter 30010.2 Vignette/Historical Notes 30110.3 Theory and Applications 30110.3.1 The Basics 30110.3.2 Equivalent Definitions of a Gaussian Vector 30310.3.3 Uncorrelated Components and Independence 30910.3.4 The Density of a Gaussian Vector 31310.3.5 Cochran's Theorem 31610.3.6 Matrix Diagonalization and Gaussian Vectors 319Exercises 32511 Convergence Types. Almost Sure Convergence. Lp-Convergence. Convergence in Probability 33811.1 Introduction/Purpose of the Chapter 33811.2 Vignette/Historical Notes 33911.3 Theory and Applications: Types of Convergence 33911.3.1 Traditional Deterministic Convergence Types 33911.3.2 Convergence of Moments of an r.v.—Convergence in Lp 34111.3.3 Almost Sure (a.s.) Convergence 34211.3.4 Convergence in Probability 34411.4 Relationships Between Types of Convergence 34611.4.1 a.s. and Lp 34711.4.2 Probability and a.s./Lp 35111.4.3 Uniform Integrability 357Exercises 35912 Limit Theorems 37212.1 Introduction/Purpose of the Chapter 37212.2 Vignette/Historical Notes 37212.3 Theory and Applications 37512.3.1 Weak Convergence 37512.3.2 The Law of Large Numbers 38412.4 Central Limit Theorem 401Exercises 40913 Appendix A: Integration Theory. General Expectations 42113.1 Integral of Measurable Functions 42213.1.1 Integral of Simple (Elementary) Functions 42213.1.2 Integral of Positive Measurable Functions 42413.1.3 Integral of Measurable Functions 42813.2 General Expectations and Moments of a Random Variable 42913.2.1 Moments and Central Moments. Lp Space 43013.2.2 Variance and the Correlation Coefficient 43113.2.3 Convergence Theorems 43314 Appendix B: Inequalities Involving Random Variables and Their Expectations 43414.1 Functions of Random Variables. The Transport Formula 441Bibliography 445Index 447
Review
"On the whole, the book has two features that set it apart from similar books: the full solutions and the examples from finance. It is up to you to decide if that makes it worth your time checking it out." (Mathematical Association of America, 1 November 2014)
Long Description
The complete collection necessary for A CONCRETE understanding of probability Written 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 Space Random Variables Characteristic Function Gaussian Random Vectors Limit Theorems Probability Measure Random Vectors in Rn Moment Generating Function Convergence Types The 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.
Review Text
?On the whole, the book has two features that set it apart from similar books: the full solutions and the examples from finance. It is up to you to decide if that makes it worth your time checking it out.? (Mathematical Association of America, 1 November 2014) Â
Review Quote
"On the whole, the book has two features that set it apart from similar books: the full solutions and the examples from finance. It is up to you to decide if that makes it worth your time checking it out." ( Mathematical Association of America , 1 November 2014)
Details ISBN0470647272 Author Ciprian A. Tudor Short Title HANDBK OF PROBABILITY Language English ISBN-10 0470647272 ISBN-13 9780470647271 Media Book Format Hardcover Affiliation Stevens Institute of Technology Series Wiley Handbooks in Applied Statistics Year 2013 DEWEY 519.2 Edition 1st Country of Publication United States Place of Publication New York Series Number 1 UK Release Date 2013-12-20 AU Release Date 2013-10-25 NZ Release Date 2013-10-25 Pages 472 Publisher John Wiley & Sons Inc Publication Date 2013-12-20 Imprint John Wiley & Sons Inc Illustrations Tables: 175 B&W, 0 Color; Graphs: 125 B&W, 0 Color Audience Professional & Vocational US Release Date 2013-12-20 We've got this
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