Theory of probability. (1997)

• Record Type: Book
• Uniform Title: Kurs teorii vero'atnostei.
• Further Information: Note: Boris V. Gnedenko ; translated from the Russian by Igor A. Ushakov.
• Authors: Gnedenko, B. V (Boris Vladimirovich), 1912-1995
• Other Names: Ushakov, Igor A translator.
• Contents: Cover -- Half Title -- Title Page -- Copyright Page -- Table of Contents -- Translator's Preface -- Author's Preface to the English Translation of the Russian Sixth Edition -- Author's Preface to the Russian Sixth Edition -- From the Author's Preface to the Russian First Edition -- Foreword -- Biography -- 1: INTRODUCTION -- 2: RANDOM EVENTS AND TIIEIR PROBABILITIES -- 1 Intuitive Understanding of Random Events -- 2 Sample Space. Classical Definition of Probability -- 3 Examples -- 4 Geometrical Probability -- 5 On Statistical Estimation of Unknown Probability -- 6 Axiomatic Construction of the Theory of Probability -- 7 Conditional Probability and the Simplest Basic Formulae -- 8 Examples -- 9 Exercises -- 3: SEQUENCES OF INDEPENDENT TRIALS -- 10 Introduction -- 11 The Local Limit Theorem -- 12 The Integral Limit Theorem -- 13 Applications of the Integral Theorem of DeMoivre-Laplace -- 14 Poisson's Theorem -- 15 Illustration of the Scheme of Independent Trials -- 16 Exercises -- 4: MARKOV CHAINS -- 17 Definition of a Markov Chain -- 18 Transition Matrix -- 19 Theorem on Limiting Probabilities -- 20 Exercises -- 5: RANDOM VARIABLES AND DISTRIBUTION FUNCTIONS -- 21 Fundamental Properties of Distribution Functions -- 22 Continuous and Discrete Distributions -- 23 Multidimensional Distribution Functions -- 24 Functions of Random Variables -- 25 The Stieltjes Integral -- 26 Exercises -- 6: NUMERICAL CHARACTERISTICS OF RANDOM VARIABLES -- 27 Mathematical Expectation -- 28 Variance -- 29 Theorems on Mathematical Expectation and Variance -- 30 Moments -- 31 Exercises -- 7: THE LAW OF LARGE NUMBERS -- 32 Mass Phenomenon and the Law of Large Numbers -- 33 Chebyshev's Form of the Law of Large Numbers -- 34 A Necessary and Sufficient Condition for the Law of Large Numbers -- 35 The Strong Law of Large Numbers -- 36 Glivenko's Theorem -- 37 Exercises. 8: CHARACTERISTIC FUNCTIONS -- 38 The Definition and Simplest Properties of Characteristic Functions -- 39 The Inversion Formula and the Uniqueness Theorem -- 40 Helly's Theorem -- 41 Limit Theorems for Characteristic Functions -- 42 Positive-Semidefinite Functions -- 43 Characteristic Functions of Multi-Dimensional Random Variables -- 44 Laplace-Stieltjes Transform -- 45 Exercises -- 9: THE CLASSICAL LIMIT THEOREM -- 46 Statement of the Problem -- 47 Lindebergʼs Theorem -- 48 The Local Limit Theorem -- 49 Exercises -- 10: THE THEORY OF INFINITELY DIVISIBLE DISTRIBUTIONS -- 50 Infinitely Divisible Distributions and Their Fundamental Properties -- 51 Canonical Representation of Infinitely Divisible Distributions -- 52 A Limit Theorem for lnfinitely Divisible Distributions -- 53 Limit Theorems for Sums: Formulation of the Problem -- 54 Limit Theorems for Sums -- 55 Conditions for Convergence to the Normal and Poisson Distributions -- 56 Sum of a Random Number of Random Variables -- 57 Exercises -- 11: THE THEORY OF STOCHASTIC PROCESSES -- 58 Introduction -- 59 The Poisson Process -- 60 Death and Birth Processes -- 61 Conditional Distribution Functions and Bayes' Formula -- 62 The Generalized Markov Equation -- 63 Continuous Stochastic Processes. Kolmogorov's Equations -- 64 Purely Discontinuous Stochastic Process. The Kolmogorov-Feller Equations -- 65 Homogeneous Stochastic Processes with Independent Increments -- 66 The Concept of a Stationary Stochastic Process. Khinchine's Theorem on the Correlation Coefficient -- 67 The Notion of a Stochastic Integral. Spectral Decomposition of Stationary Processes -- 68 The Birkhoff-Khinchine Ergodic lbeorem -- 12: ELEMENTS OF STATISTICS -- 69 Some Problems of Mathematical Statistics -- 70 The Classical Procedure for Estimating the Distribution Parameters -- 71 Exhaustive Statistics. 72 Confidence Limits and Confidence Probabilities -- 73 Test of Statistical Hypothesis -- APPENDIX: THE HISTORY OF PROBABILITY THEORY -- Part 1: Main Concepts of Probability and Random Event -- Part 2: Formation of the Foundation of Probability lbeory -- Part 3: Formation of the Concept of Random Variable -- Part 4: History of Stochastic Processes -- Tables of Function Values -- References -- Index.
• Edition: Sixth edition
• Publisher Details: Boca Raton, [Florida] London, [England] New York : CRC Press
• Publication Date: 1997
• Copyright Date: 1988
• Extent: 1 online resource (xxi, 497 pages), illustrations
• Subjects: 519.2; Probabilities; Electronic books
• Languages: English
• ISBNs: 9781351408585; 1351408585
• Related ISBNs: 9789056995850
• Notes: Note: Includes bibliographical references and index.; Note: Description based on print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.