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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:
Acceso en línea:Texto completo

MARC

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245 1 0 |a Probability and Stochastic Processes  |h [electronic resource]. 
260 |a Newark :  |b John Wiley & Sons, Incorporated,  |c 2014. 
300 |a 1 online resource (1165 p.). 
490 1 |a New York Academy of Sciences Ser. 
500 |a Description based upon print version of record. 
505 0 |a 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 
505 8 |a 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 
505 8 |a 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 
505 8 |a 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 
505 8 |a 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 
500 |a 9.1 General Characteristics of Stochastic Processes 
590 |a ProQuest Ebook Central  |b Ebook Central Academic Complete 
655 0 |a Electronic books. 
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830 0 |a New York Academy of Sciences Ser. 
856 4 0 |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=7103842  |z Texto completo 
938 |a ProQuest Ebook Central  |b EBLB  |n EBL7103842 
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