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Probability and stochastic processes / Ionut Florescu, Stevens Institute of Technology, Hoboken, NJ.

Author
Florescu, Ionuţ, 1973-
Published
Hoboken, New Jersey : John Wiley & Sons, Inc., [2014]
Physical Description
1 online resource
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Contents
Title Page; Copyright; Dedication; Preface; Acknowledgments; Introduction; Part I: Probability; Chapter 1: Elements of Probability Measure; 1.1 Probability Spaces; 1.2 Conditional Probability; 1.3 Independence; 1.4 Monotone Convergence Properties of Probability; 1.5 Lebesgue Measure on the Unit Interval (0,1]; Problems; Chapter 2: Random Variables; Reduction to R. Random variables; 2.1 Discrete and Continuous Random Variables; 2.2 Examples of Commonly Encountered Random Variables; 2.3 Existence of Random Variables with Prescribed Distribution. Skorohod Representation of a Random Variable., 2.4 Independence2.5 Functions of Random Variables. Calculating Distributions; Problems; Chapter 3: Applied Chapter: Generating Random Variables; 3.1 Generating One-Dimensional Random Variables by Inverting the cdf; 3.2 Generating One-Dimensional Normal Random Variables; 3.3 Generating Random Variables. Rejection Sampling Method; 3.4 Generating Random Variables. Importance Sampling; Problems; Chapter 4: Integration Theory; 4.1 Integral of Measurable Functions; 4.2 Expectations; 4.3 Moments of a Random Variable. Variance and the Correlation Coefficient., 4.4 Functions of Random Variables. The Transport Formula4.5 Applications. Exercises in Probability Reasoning; 4.6 A Basic Central Limit Theorem: The DeMoivre-LaplaceTheorem:; Problems; Chapter 5: Product Spaces. Conditional Distribution and Conditional Expectation; 5.1 Product Spaces; 5.2 Conditional Distribution and Expectation. Calculation in Simple Cases; 5.3 Conditional Expectation. General Definition; 5.4 Random Vectors. Moments and Distributions; Problems; Chapter 6: Tools to study Probability. Generating Function, Moment Generating Function, Characteristic Function., 6.1 Sums of Random Variables. Convolutions6.2 Generating Functions and Applications; 6.3 Moment Generating Function; 6.4 Characteristic Function; 6.5 Inversion and Continuity Theorems; 6.6 Stable Distributions. Lévy Distribution; Problems; Chapter 7: Limit Theorems; Introduction; 7.1 Types of Convergence; 7.2 Relationships between Types of Convergence; 7.3 Continuous Mapping Theorem. Joint Convergence. Slutsky's Theorem; 7.4 The Two Big Limit Theorems: LLN and CLT; 7.5 Extensions of Central Limit Theorem. Limit Theorems for Other Types of Statistics., and 7.6 Exchanging the Order of Limits and ExpectationsProblems; Chapter 8: Statistical Inference; 8.1 The Classical Problems in Statistics; 8.2 Parameter Estimation Problem; 8.3 Maximum Likelihood Estimation Method; 8.4 The Method of Moments; 8.5 Testing, the Likelihood Ratio Test; 8.6 Confidence Sets; Problems; Part II: Stochastic Processes; Chapter 9: Introduction to Stochastic Processes; 9.1 General Characteristics of Stochastic Processes; 9.2 A Simple Process-The Bernoulli Process; Problems; Chapter 10: The Poisson Process; Introduction; 10.1 Definitions.
Summary
A comprehensive and accessible presentation of probability and stochastic processes with emphasis on key theoretical concepts and real-world applications With a sophisticated approach, Probability and Stochastic Processes successfully balances theory and applications in a pedagogical and accessible format. The book's primary focus is on key theoretical notions in probability to provide a foundation for understanding concepts and examples related to stochastic processes. Organized into two main sections, the book begins by developing probability theory with topical coverage on probability measure; random variables; integration theory; product spaces, conditional distribution, and conditional expectations; and limit theorems. The second part explores stochastic processes and related concepts including the Poisson process, renewal processes, Markov chains, semi-Markov processes, martingales, and Brownian motion. Featuring a logical combination of traditional and complex theories as well as practices, Probability and Stochastic Processes also includes: Multiple examples from disciplines such as business, mathematical finance, and engineering Chapter-by-chapter exercises and examples to allow readers to test their comprehension of the presented material A rigorous treatment of all probability and stochastic processes concepts An appropriate textbook for probability and stochastic processes courses at the upper-undergraduate and graduate level in mathematics, business, and electrical engineering, Probability and Stochastic Processes is also an ideal reference for researchers and practitioners in the fields of mathematics, engineering, and finance.
Subject(s)
ISBN
9781118593202 (epdf)
1118593200 (epdf)
9781118593134 (epub)
1118593138 (epub)
0470624558
9780470624555
9780470624555 (cloth)
Bibliography Note
Includes bibliographical references and index.
View MARC record | catkey: 45625431