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    Probability and Stochastic Modeling

    ISBN-10: 1439872066
    ISBN-13: 9781439872062
    Author(s): Vladimir I. Rotar
    Description: With a focus on applications, this unique introductory book goes beyond the standard facts typically presented in probability texts. It includes a variety of stochastic models of real phenomena and methods of modeling, such as simulation, Markov  More...
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    List Price: $87.95
    Publisher: CRC Press LLC
    Binding: Hardcover
    Pages: 508
    Size: 7.50" wide x 10.50" long x 1.00" tall
    Weight: 2.288
    Language: English

    With a focus on applications, this unique introductory book goes beyond the standard facts typically presented in probability texts. It includes a variety of stochastic models of real phenomena and methods of modeling, such as simulation, Markov chains, counting and compound processes, simple trees, queuing theory, reliability models, diffusion, and models of the financial market. It contains numerous examples from various fields, including economics, finance, insurance, computer science, and physics. The text also provides examples and exercises on numerical calculations using Excel.

    Basic Notions
    Sample Space and Events
    Counting Techniques
    Independence and Conditional Probability
    The Borel-Cantelli Theorem
    Discrete Random Variables
    Random Variables and Vectors
    Expected Value
    Variance and Other Moments
    Inequalities for Deviations
    Some Basic Distributions
    Convergence of Random Variables
    The Law of Large Numbers
    Conditional Expectation
    Generating Functions
    Branching Processes
    Random Walk Revisited
    Branching Processes
    Generating Functions
    Branching Processes Revisited
    More on Random Walk
    Markov Chains
    Definitions and Examples
    Probability Distributions of Markov Chains
    The First Step Analysis
    Passage Times
    Variables Defined on a Markov Chain
    Ergodicity and Stationary Distributions
    A Classification of States and Ergodicity
    Continuous Random Variables
    Continuous Distributions
    Some Basic Distributions
    Continuous Multivariate Distributions
    Sums of Independent Random Variables
    Conditional Distributions and Expectations
    Distributions in the General Case
    Distribution Functions
    Expected Values
    On Convergence in Distribution and Probability
    Moment Generating Functions
    Definitions and Properties
    Some Examples of Applications
    Exponential or Bernstein-Chernoff's Bounds
    The Central Limit Theorem for Independent Random Variables
    The Central Limit Theorem (CLT) for Independent and Identically Distributed Random Variables
    The CLT for Independent Variables in the General Case
    Covariance Analysis
    The Multivariate Normal Distribution
    The Multivariate Central Limit Theorem
    Covariance and Correlation
    Covariance Matrices and Some Applications
    The Multivariate Normal Distribution
    Maxima and Minima of Random Variables
    Elements of Reliability Theory
    Hazard Rate and Survival Probabilities
    Maxima and Minima of Random Variables
    Reliability Characteristics
    Limit Theorems for Maxima and Minima
    Hazard Rate
    Survival Probabilities
    Stochastic Processes: Preliminaries
    A General Definition
    Processes with Independent Increments
    Brownian Motion
    Markov Processes
    A Representation and Simulation of Markov Processes in Discrete Time
    Counting and Queuing Processes
    Birth and Death Processes: A General Scheme
    Poisson Processes
    Birth and Death Processes
    Elements of Renewal Theory
    Limit Theorems
    Some Proofs
    Martingales in Discrete Time
    Definitions and Properties
    Optional Time and Some Applications
    Martingales and a Financial Market Model
    Limit Theorems for Martingales
    Brownian Motion and Martingales in Continuous Time
    Brownian Motion and Its Generalizations
    Martingales in Continuous Time
    More on Dependency Structures
    Arrangement Structures and the Corresponding Dependencies
    Measures of Dependency
    Limit Theorems for Dependent Random Variables
    Symmetric Distributions
    De Finetti's Theorem
    Comparison of Random Variables
    Risk Evaluation
    Some Particular Criteria
    Expected Utility
    Generalizations of the EUM Criterion
    Answers to Exercises
    Exercises appear at the end of each chapter

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