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Introduction to Probability and Stochastic Processes with Applications [Hardback]

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  • Formāts: Hardback, 614 pages, height x width x depth: 231x155x46 mm, weight: 1179 g
  • Izdošanas datums: 27-Jul-2012
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1118294408
  • ISBN-13: 9781118294406
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Introduction to Probability and Stochastic Processes with ApplicationsPalielināt
  • Formāts: Hardback, 614 pages, height x width x depth: 231x155x46 mm, weight: 1179 g
  • Izdošanas datums: 27-Jul-2012
  • Izdevniecība: John Wiley & Sons Inc
  • ISBN-10: 1118294408
  • ISBN-13: 9781118294406
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781118294406.html
Keywords:
An easily accessible, real-world approach to probability and stochastic processes

Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic techniques to accurately model these phenomena.

The authors discuss a broad range of topics, from the basic concepts of probability to advanced topics for further study, including Itō integrals, martingales, and sigma algebras. Additional topical coverage includes:





Distributions of discrete and continuous random variables frequently used in applications Random vectors, conditional probability, expectation, and multivariate normal distributions The laws of large numbers, limit theorems, and convergence of sequences of random variables Stochastic processes and related applications, particularly in queueing systems Financial mathematics, including pricing methods such as risk-neutral valuation and the Black-Scholes formula

Extensive appendices containing a review of the requisite mathematics and tables of standard distributions for use in applications are provided, and plentiful exercises, problems, and solutions are found throughout. Also, a related website features additional exercises with solutions and supplementary material for classroom use. Introduction to Probability and Stochastic Processes with Applications is an ideal book for probability courses at the upper-undergraduate level. The book is also a valuable reference for researchers and practitioners in the fields of engineering, operations research, and computer science who conduct data analysis to make decisions in their everyday work.

Recenzijas

A great strength of this book is the enormous number of detailed examples and the exercises at the end of each chapter, many of which include solutions. The writing style is very clear, because the authors brought their experiences in teaching for several years to its writing. . .In summary, the first eight chapters provide an excellent introduction to and quick overview of probability theory, with many examples.  (Interfaces, 1 September 2013)

The choice of material and the presentation make this book an excellent first introduction into probability theory and stochastic processes from upper undergraduate level onwards in all the areas mentioned above. It may also serve math students at the very initial stages of their studies as a stepping stone to get a sound grasp of some basic concepts of probability.  (Contemporary Physics, 13 August 2012)

 

 

Foreword xiii
Preface xv
Acknowledgments xvii
Introduction xix
1 Basic Concepts
1(4)
1.1 Probability Space
1(13)
1.2 Laplace Probability Space
14(5)
1.3 Conditional Probability and Event Independence
19(16)
1.4 Geometric Probability
35(2)
Exercises
37
2 Random Variables and Their Distributions
5(110)
2.1 Definitions and Properties
51(11)
2.2 Discrete Random Variables
62(5)
2.3 Continuous Random Variables
67(5)
2.4 Distribution of a Function of a Random Variable
72(8)
2.5 Expected Value and Variance of a Random Variable
80(35)
Exercises
101(14)
3 Some Discrete Distributions
115(30)
3.1 Discrete Uniform, Binomial and Bernoulli Distributions
115(8)
3.2 Hypergeometric and Poisson Distributions
123(10)
3.3 Geometric and Negative Binomial Distributions
133(12)
Exercises
138(7)
4 Some Continuous Distributions
145(46)
4.1 Uniform Distribution
145(6)
4.2 Normal Distribution
151(10)
4.3 Family of Gamma Distributions
161(9)
4.4 Weibull Distribution
170(2)
4.5 Beta Distribution
172(3)
4.6 Other Continuous Distributions
175(16)
Exercises
181(10)
5 Random Vectors
191(74)
5.1 Joint Distribution of Random Variables
191(19)
5.2 Independent Random Variables
210(7)
5.3 Distribution of Functions of a Random Vector
217(11)
5.4 Covariance and Correlation Coefficient
228(7)
5.5 Expected Value of a Random Vector and Variance-Covariance Matrix
235(5)
5.6 Joint Probability Generating, Moment Generating and Characteristic Functions
240(25)
Exercises
251(14)
6 Conditional Expectation
265(30)
6.1 Conditional Distribution
265(15)
6.2 Conditional Expectation Given a σ-Algebra
280(15)
Exercises
287(8)
7 Multivariate Normal Distributions
295(18)
7.1 Multivariate Normal Distribution
295(7)
7.2 Distribution of Quadratic Forms of Multivariate Normal Vectors
302(11)
Exercises
308(5)
8 Limit Theorems
313(26)
8.1 The Weak Law of Large Numbers
313(6)
8.2 Convergence of Sequences of Random Variables
319(4)
8.3 The Strong Law of Large Numbers
323(6)
8.4 Central Limit Theorem
329(10)
Exercises
333(6)
9 Introduction to Stochastic Processes
339(78)
9.1 Definitions and Properties
340(4)
9.2 Discrete-Time Markov Chain
344(27)
9.2.1 Classification of States
353(15)
9.2.2 Measure of Stationary Probabilities
368(3)
9.3 Continuous-Time Markov Chains
371(10)
9.4 Poisson Process
381(8)
9.5 Renewal Processes
389(11)
9.6 Semi-Markov Process
400(17)
Exercises
406(11)
10 Introduction to Queueing Models
417(44)
10.1 Introduction
417(2)
10.2 Markovian Single-Server Models
419(12)
10.2.1 M/M/1/∞ Queueing System
419(8)
10.2.2 M/M/1/N Queueing System
427(4)
10.3 Markovian MultiServer Models
431(9)
10.3.1 M/M/c/∞ Queueing System
431(5)
10.3.2 M/M/c/c Loss System
436(2)
10.3.3 M/M/c/K Finite-Capacity Queueing System
438(1)
10.3.4 M/M/∞ Queueing System
439(1)
10.4 Non-Markovian Models
440(21)
10.4.1 M/G/1 Queueing System
441(4)
10.4.2 GI/M/1 Queueing System
445(3)
10.4.3 M/G/1/N Queueing System
448(4)
10.4.4 GI/M/1/N Queueing System
452(5)
Exercises
457(4)
11 Stochastic Calculus
461(36)
11.1 Martingales
461(11)
11.2 Brownian Motion
472(9)
11.3 Ito Calculus
481(16)
Exercises
491(6)
12 Introduction to Mathematical Finance
497(36)
12.1 Financial Derivatives
498(6)
12.2 Discrete-Time Models
504(13)
12.2.1 The Binomial Model
509(3)
12.2.2 Multi-Period Binomial Model
512(5)
12.3 Continuous-Time Models
517(10)
12.3.1 Black-Scholes Formula European Call Option
521(4)
12.3.2 Properties of Black-Scholes Formula
525(2)
12.4 Volatility
527(6)
Exercises
529(4)
Appendix A Basic Concepts on Set Theory
533(6)
Appendix B Introduction to Combinatorics
539(10)
Exercises
546(3)
Appendix C Topics on Linear Algebra
549(2)
Appendix D Statistical Tables
551(12)
D.1 Binomial Probabilities
551(6)
D.2 Poisson Probabilities
557(2)
D.3 Standard Normal Distribution Function
559(1)
D.4 Chi-Square Distribution Function
560(3)
Selected Problem Solutions 563(14)
References 577(4)
Glossary 581(4)
Index 585
LILIANA BLANCO CASTAŃEDA, DrRerNat, is Associate Professor in the Department of Statistics at the National University of Colombia and the author of several journal articles and three books on basic and advanced probability.

VISWANATHAN ARUNACHALAM, PhD, is Associate Professor in the Department of Mathematics at the Universidad de los Andes, Colombia. He has published numerous journal articles in areas such as optimization, stochastic processes, and the mathematics of financial derivatives.

SELVAMUTHU DHARMARAJA, PhD, is Associate Professor in the Department of Mathematics and the Bharti School of Telecommunication Technology and Management at the Indian Institute of Technology Delhi. The author of several journal articles, he is Associate Editor for the International Journal of Communication Systems.