Probability and Stochastic Processes

Detalles Bibliográficos
Autor principal: Florescu, Ionut
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2014.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • 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 Independence
  • 2.5 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 Formula
  • 4.5 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. Convolutions
  • 6.2 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
  • 7.6 Exchanging the Order of Limits and Expectations
  • Problems
  • 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

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