Introduction to probability and stochastic processes with applications

This text book is designed for a one-year course in probability and stochastic processes with applications, especially for students who wish to specialize in probabilistic modeling. This book bridges the gap between elementary texts and advanced texts in probability and is easily accessible for students with diverse backgrounds and majoring in engineering, applied sciences, business andfinance, statistics, mathematics, and operations research. The text contains many examples and exercises which have been tested in classrooms and are chosen from diverse areas such as queuing models, reliability and finance. Chapter coverage includes: basic concepts; random variables and their distributions; discrete distributions; continuous distributions; random vectors; multivariate normal distributions; conditional expectation; limit theorems; stochastic processes; queuing models; stochastic calculus; and mathematical finance. INDICE: Foreword xiiiPreface xvAcknowledgments xviiIntroduction xix1. Basic Concepts 11.1 Probability Space 11.2 Laplace Probability Space 131.3 Conditional Probability and Event Independence 181.4 Geometric Probability 34Exercises 362. Random Variables and their Distributions 492.1 Definitions and Properties 492.2 Discrete Random Variables 592.3 Continuous Random Variables 642.4 Distribution of a Function of a Random Variable 692.5 Expected Value and Varianceof a Random Variable 77Exercises 973. Some Discrete Distributions 1113.1 Discrete Uniform, Binomial and Bernoulli Distributions 1113.2 Hypergeometric and Poisson Distributions 1193.3 Geometric and Negative Binomial Distributions 128Exercises 1334. Some Continuous Distributions 1414.1 Uniform Distribution 1414.2 Normal Distribution 1474.3 Family of Gamma Distribution 1584.4 Weibull Distribution 1674.5 Beta Distribution 1694.6 Other Continuous Distributions 173Exercises 1785. Random Vectors 1895.1 Joint Distribution of Random Variables 1895.2 Independent Random Variables 2065.3 Distribution of Functions of a Random Vector 2145.4 Covariance and Correlation Coefficient 2245.5 Expected Value and Variance of a Random Vector 2325.6 Generating Functions 236Exercises 2476. Conditional Expectation 2616.1 Conditional Distribution 2616.2 Conditional Expectation given a ?-algebra 276Exercises 2837. Multivariate Normal Distribution 2917.1 Multivariate Normal Distribution 2917.2 Distribution of Quadratic Forms ofMultivariate Normal Vectors 298Exercises 3048. Limit Theorems 3078.1 The WeakLaw of Large Numbers 3078.2 Convergence of Sequences of Random Variables 3138.3 The Strong Law of Large Numbers 3168.4 Central Limit Theorem 323Exercises 3289. Introduction to Stochastic Processes 3339.1 Definitions and Properties 3349.2 Discrete Time Markov Chain 3389.3 Continuous Time Markov Chains 3649.4 Poisson Process 3749.5 Renewal Processes 3839.6 Semi-Markov process 393Exercises39910. Introduction to Queueing Models 40910.1 Introduction 40910.2 MarkovianSingle Server Models 41110.3 Markovian Multi Server Models 42310.4 Non-Markovian Models 432Exercises 44911. Stochastic Calculus 45311.1 Martingales 45311.2Brownian Motion 46411.3 Itô Calculus 473Exercises 48412. Introduction to Mathematical Finance 48912.1 Financial Derivatives 49012.2 Discrete-time Models 49612.3 Continuous-time models 51312.4 Volatility 523Exercises 525Appendix A. Basic Concepts on Set Theory 529Appendix B. Introduction to Combinatorics 535Appendix C. Topics on Linear Algebra 545Appendix D. Statistical Tables 547ProblemSolutions 559References 575Bibliography 575Glossary 579Index 583

• ISBN: 978-1-118-29440-6
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 614
• Fecha Publicación: 22/06/2012
• Nº Volúmenes: 1
• Idioma: Inglés