Catalogue


Introduction to probability and stochastic processes with applications [electronic resource] /
Liliana Blanco Castañeda, Viswanathan Arunachalam, Delvamuthu [sic] Dharmaraja.
imprint
Hoboken, NJ : Wiley, 2012.
description
xxiii, 589 p. : ill. ; 24 cm.
ISBN
9781118294406 (hardback)
format(s)
Book
More Details
imprint
Hoboken, NJ : Wiley, 2012.
isbn
9781118294406 (hardback)
restrictions
Licensed for access by U. of T. users.
abstract
"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 and finance, 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"--
catalogue key
8578243
 
Includes bibliographical references (p. 577-579) and index.
A Look Inside
About the Author
Author Affiliation
Liliana Blanco Castaeda, 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.
Reviews
Review Quotes
"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)
This item was reviewed in:
Reference & Research Book News, August 2012
To find out how to look for other reviews, please see our guides to finding book reviews in the Sciences or Social Sciences and Humanities.
Summaries
Bowker Data Service Summary
This text is designed for a one-year course in probability and stochastic processes with applications, especially for students who wish to specialize in probabilistic modeling.
Long Description
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 Itô 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.
Main Description
This book develops the basic concepts of probability, random variables, standard discrete and continuous distributions, joint probability distributions, laws of large numbers, the central limit theorem, and financial mathematics. Statistical inference and its application in stochastic processes, in particular to queueing systems, is also addressed. The presented theory is illustrated with many current real world examples and applications. This book reinforces and extends the material typically covered in introductory probability courses and is specifically written and accessible for an introductory probability course including students with diverse backgrounds and majoring in engineering, the applied sciences, business and finance, statistics, mathematics, and/or operations research. Chapter coverage includes: basic concepts; random variables and their distributions; discrete distributions; continuous distributions; random vectors; functions and multivariate normal distributions; conditional expected value and martingales; limit theorems; statistical inference; stochastic calculus; and mathematical calculus.
Main Description
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 and finance, 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.
Table of Contents
Forewordp. xiii
Prefacep. xv
Acknowledgmentsp. xvii
Introductionp. xix
Basic Conceptsp. 1
Probability Spacep. 1
Laplace Probability Spacep. 14
Conditional Probability and Event Independencep. 19
Geometric Probabilityp. 35
Exercisesp. 37
Random Variables and Their Distributionsp. 51
Definitions and Propertiesp. 51
Discrete Random Variablesp. 62
Continuous Random Variablesp. 67
Distribution of a Function of a Random Variablep. 72
Expected Value and Variance of a Random Variablep. 80
Exercisesp. 101
Some Discrete Distributionsp. 115
Discrete Uniform, Binomial and Bernoulli Distributionsp. 115
Hypergeometric and Poisson Distributionsp. 123
Geometric and Negative Binomial Distributionsp. 133
Exercisesp. 138
Some Continuous Distributionsp. 145
Uniform Distributionp. 145
Normal Distributionp. 151
Family of Gamma Distributionsp. 161
Weibull Distributionp. 170
Beta Distributionp. 172
Other Continuous Distributionsp. 175
Exercisesp. 181
Random Vectorsp. 191
Joint Distribution of Random Variablesp. 191
Independent Random Variablesp. 210
Distribution of Functions of a Random Vectorp. 217
Covariance and Correlation Coefficientp. 228
Expected Value of a Random Vector and Variance-Covariance Matrixp. 235
Joint Probability Generating, Moment Generating and Characteristic Functionsp. 240
Exercisesp. 251
Conditional Expectationp. 265
Conditional Distributionp. 265
Conditional Expectation Given a ¿-Algebrap. 280
Exercisesp. 287
Multivariate Normal Distributionsp. 295
Multivariate Normal Distributionp. 295
Distribution of Quadratic Forms of Multivariate Normal-Vectorsp. 302
Exercisesp. 308
Limit Theoremsp. 313
The Weak Law of Large Numbersp. 313
Convergence of Sequences of Random Variablesp. 319
The Strong Law of Large Numbersp. 323
Central Limit Theoremp. 329
Exercisesp. 333
Introduction to Stochastic Processesp. 339
Definitions and Propertiesp. 340
Discrete-Time Markov Chainp. 344
Classification of Statesp. 353
Measure of Stationary Probabilitiesp. 368
Continuous-Time Markov Chainsp. 371
Poisson Processp. 381
Renewal Processesp. 389
Semi-Markov Processp. 400
Exercisesp. 406
Introduction to Queueing Modelsp. 417
Introductionp. 417
Markovian Single-Server Modelsp. 419
M/M/1/∞ Queueing Systemp. 419
M/M/1/N Queueing Systemp. 427
Markovian MultiServer Modelsp. 431
M/M/c/∞ Queueing Systemp. 431
M/M/c/c Loss Systemp. 436
M/M/c/K Finite-Capacity Queueing Systemp. 438
M/M/∞ Queueing Systemp. 439
Non-Markovian Modelsp. 440
M/G/1 Queueing Systemp. 441
GI/M/1 Queueing Systemp. 445
M/G/1/N Queueing Systemp. 448
GI/M/1/N Queueing Systemp. 452
Exercisesp. 457
Stochastic Calculusp. 461
Martingalesp. 461
Brownian Motionp. 472
Itô Calculusp. 481
Exercisesp. 491
Introduction to Mathematical Financep. 497
Financial Derivativesp. 498
Discrete-Time Modelsp. 504
The Binomial Modelp. 509
Multi-Period Binomial Modelp. 512
Continuous-Time Modelsp. 517
Black-Scholes Formula European Call Optionp. 521
Properties of Black-Scholes Formulap. 525
Volatilityp. 527
Exercisesp. 529
Basic Concepts on Set Theoryp. 533
Introduction to Combinatoricsp. 539
Exercisesp. 546
Topics on Linear Algebrap. 549
Statistical Tablesp. 551
Binomial Probabilitiesp. 551
Poisson Probabilitiesp. 557
Standard Normal Distribution Functionp. 559
Chi-Square Distribution Functionp. 560
Selected Problem Solutionsp. 563
Referencesp. 577
Glossaryp. 581
Indexp. 585
Table of Contents provided by Ingram. All Rights Reserved.

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