An Introduction to Probability :Theory and its Applications Vol - ll
Feller, William
An Introduction to Probability :Theory and its Applications Vol - ll - 2nd - New Delhi Wiley India 1971 - 669p.
1 The Exponential and the Uniform Densities
Densities Convolutions
The Exponential Density
Waiting Time Paradoxes The Poisson Process
The Persistence of Bad Luck
Waiting Times and Order Statistics
The Uniform Distribution
Random Splittings
Terminating Transient Processes
Diverse Applications
Existence of Limits in Stochastic Processes
9 Renewal Theory on the Whole Line
Problems for Solution
Random Walks in 311
Basic Concepts and Notations
Duality Types of Random Walks
Convolutions and Covering Theorems
Random Directions
The Use of Lebesgue Measure
Empirical Distributions
Problems for Solution
Special Densities Randomization
Gamma Distributions
3 Related Distributions of Statistics
Some Common Densities
Randomization and Mixtures
Discrete Distributions
CHAPTER
chapter
CHAPTER
Symmetrization
Integration by Parts Existence of Moments
Chebyshevs Inequality
Further Inequalities Convex Functions
Simple Conditional Distributions Mixtures
Starred sections are not required for the understanding of the sequel and should be omitted at first readme
11 Conditional Expectations
Problems for Solution
A Survey of some Important Distributions and Processes
Examples
Infinitely Divisible Distributions in Rl
Processes with Independent Increments
5 Ruin Problems in Compound Poisson Processes
Renewal Processes
Examples and Problems
Random Walks
The Queuing Process
Persistent and Transient Random Walks
General Markov Chains
12 Martingales
Problems for Solution
Laws of Large Numbers Applications in Analysis
Bernstein Polynomials Absolutely Monotone Functions
Moment Problems
4 Application to Exchangeable Variables
5 Generalized Taylor Formula and SemiGroups
Inversion Formulas for Laplace Transforms
7 Laws of Large Numbers for Identically Distributed Variables
8 Strong Laws
9 Generalization to Martingales
Problems for Solution
The Basic Limit Theorems
Special Properties
Distributions as Operators
The Central Limit Theorem
5 Infinite Convolutions
Selection Theorems
7 Ergodic Theorems for Markov Chains
Regular Variation
9 Asymptotic Properties of Regularly Varying Functions
Problems for Solution
chapter K Infinitely Divisible Distributions and SemiGroups
Convolution SemiGroups
Preparatory Lemmas
Finite Variances
The Main Theorems
Stable SemiGroups
Triangular Arrays with Identical Distributions
Domains of Attraction
Variable Distributions The ThreeSeries Theorem
Problems for Solution
Markov Processes and SemiGroups
The PseudoPoisson Type
Linear Increments
Jump Processes
Diffusion Processes in 311
The Forward Equation Boundary Conditions
Diffusion in Higher Dimensions
Subordinated Processes
Markov Processes and SemiGroups
The Exponential Formula of SemiGroup Theory
Generators The Backward Equation
Renewal Theory
Proof of the Renewal Theorem
3 Refinements
Persistent Renewal Processes
The Number Nt of Renewal Epochs
Distribution of Ladder Heights WienerHopf Factor ization
3a The WienerHopf Integral Equation
Examples
Applications
A Combinatorial Lemma
Distribution of Ladder Epochs
The Arc Sine Laws
Miscellaneous Complements
Problems for Solution
Laplace Transforms Tauberian Theorems Resolvents
Elementary Properties
Examples
Completely Monotone Functions Inversion Formulas
Tauberian Theorems
6 Stable Distributions
7 Infinitely Divisible Distributions
8 Higher Dimensions
Laplace Transforms for SemiGroups
The HilleYosida Theorem
Problems for Solution
Applications of Laplace Transforms
Examples
Limit Theorems Involving Arc Sine Distributions
Busy Periods and Related Branching Processes
Diffusion Processes
BirthandDeath Processes and Random Walks
The Kolmogorov Differential Equations
The Pure Birth Process
Calculation of Ergodic Limits and of FirstPassage Times
Problems for Solution
Characteristic Functions
Special Distributions Mixtures
2a Some Unexpected Phenomena
Uniqueness Inversion Formulas
Regularity Properties
The Central Limit Theorem for Equal Components
The Lindeberg Conditions
Characteristic Functions in Higher Dimensions
8 Two Characterizations of the Normal Distribution
Problems for Solution
CHAPTER XVI Expansions Related to the Central Limit Theorem
Notations
Expansions for Densities
Smoothing
Expansions for Distributions
The BerryEsseen Theorems
Expansions in the Case of Varying Components
Large Deviations
Infinitely Divisible Distributions
Canonical Forms The Main Limit Theorem
2a Derivatives of Characteristic Functions
Examples and Special Properties
Special Properties
Stable Distributions and Their Domains of Attraction
6 Stable Densities
Triangular Arrays
8 The Class L
9 Partial Attraction Universal Laws
10 Infinite Convolutions
Higher Dimensions
Problems for Solution
Applications of Fourier Methods to Random Walks
2 Finite Intervals Walds Approximation
The WienerHopf Factorization
Implications and Applications
Two Deeper Theorems
Criteria for Persistency
Problems for Solution
Harmonic Analysis
Positive Definite Functions
Stationary Processes
Fourier Series
5 The Poisson Summation Formula
Positive Definite Sequences
L2 Theory
Stochastic Processes and Integrals
Problems for Solution
Answers to Problems
Some Books on Cognate Subjects
Index
Copyright
9788126518067
Probabilities and applied mathematics
519.2 FEL - I;Vol-II
An Introduction to Probability :Theory and its Applications Vol - ll - 2nd - New Delhi Wiley India 1971 - 669p.
1 The Exponential and the Uniform Densities
Densities Convolutions
The Exponential Density
Waiting Time Paradoxes The Poisson Process
The Persistence of Bad Luck
Waiting Times and Order Statistics
The Uniform Distribution
Random Splittings
Terminating Transient Processes
Diverse Applications
Existence of Limits in Stochastic Processes
9 Renewal Theory on the Whole Line
Problems for Solution
Random Walks in 311
Basic Concepts and Notations
Duality Types of Random Walks
Convolutions and Covering Theorems
Random Directions
The Use of Lebesgue Measure
Empirical Distributions
Problems for Solution
Special Densities Randomization
Gamma Distributions
3 Related Distributions of Statistics
Some Common Densities
Randomization and Mixtures
Discrete Distributions
CHAPTER
chapter
CHAPTER
Symmetrization
Integration by Parts Existence of Moments
Chebyshevs Inequality
Further Inequalities Convex Functions
Simple Conditional Distributions Mixtures
Starred sections are not required for the understanding of the sequel and should be omitted at first readme
11 Conditional Expectations
Problems for Solution
A Survey of some Important Distributions and Processes
Examples
Infinitely Divisible Distributions in Rl
Processes with Independent Increments
5 Ruin Problems in Compound Poisson Processes
Renewal Processes
Examples and Problems
Random Walks
The Queuing Process
Persistent and Transient Random Walks
General Markov Chains
12 Martingales
Problems for Solution
Laws of Large Numbers Applications in Analysis
Bernstein Polynomials Absolutely Monotone Functions
Moment Problems
4 Application to Exchangeable Variables
5 Generalized Taylor Formula and SemiGroups
Inversion Formulas for Laplace Transforms
7 Laws of Large Numbers for Identically Distributed Variables
8 Strong Laws
9 Generalization to Martingales
Problems for Solution
The Basic Limit Theorems
Special Properties
Distributions as Operators
The Central Limit Theorem
5 Infinite Convolutions
Selection Theorems
7 Ergodic Theorems for Markov Chains
Regular Variation
9 Asymptotic Properties of Regularly Varying Functions
Problems for Solution
chapter K Infinitely Divisible Distributions and SemiGroups
Convolution SemiGroups
Preparatory Lemmas
Finite Variances
The Main Theorems
Stable SemiGroups
Triangular Arrays with Identical Distributions
Domains of Attraction
Variable Distributions The ThreeSeries Theorem
Problems for Solution
Markov Processes and SemiGroups
The PseudoPoisson Type
Linear Increments
Jump Processes
Diffusion Processes in 311
The Forward Equation Boundary Conditions
Diffusion in Higher Dimensions
Subordinated Processes
Markov Processes and SemiGroups
The Exponential Formula of SemiGroup Theory
Generators The Backward Equation
Renewal Theory
Proof of the Renewal Theorem
3 Refinements
Persistent Renewal Processes
The Number Nt of Renewal Epochs
Distribution of Ladder Heights WienerHopf Factor ization
3a The WienerHopf Integral Equation
Examples
Applications
A Combinatorial Lemma
Distribution of Ladder Epochs
The Arc Sine Laws
Miscellaneous Complements
Problems for Solution
Laplace Transforms Tauberian Theorems Resolvents
Elementary Properties
Examples
Completely Monotone Functions Inversion Formulas
Tauberian Theorems
6 Stable Distributions
7 Infinitely Divisible Distributions
8 Higher Dimensions
Laplace Transforms for SemiGroups
The HilleYosida Theorem
Problems for Solution
Applications of Laplace Transforms
Examples
Limit Theorems Involving Arc Sine Distributions
Busy Periods and Related Branching Processes
Diffusion Processes
BirthandDeath Processes and Random Walks
The Kolmogorov Differential Equations
The Pure Birth Process
Calculation of Ergodic Limits and of FirstPassage Times
Problems for Solution
Characteristic Functions
Special Distributions Mixtures
2a Some Unexpected Phenomena
Uniqueness Inversion Formulas
Regularity Properties
The Central Limit Theorem for Equal Components
The Lindeberg Conditions
Characteristic Functions in Higher Dimensions
8 Two Characterizations of the Normal Distribution
Problems for Solution
CHAPTER XVI Expansions Related to the Central Limit Theorem
Notations
Expansions for Densities
Smoothing
Expansions for Distributions
The BerryEsseen Theorems
Expansions in the Case of Varying Components
Large Deviations
Infinitely Divisible Distributions
Canonical Forms The Main Limit Theorem
2a Derivatives of Characteristic Functions
Examples and Special Properties
Special Properties
Stable Distributions and Their Domains of Attraction
6 Stable Densities
Triangular Arrays
8 The Class L
9 Partial Attraction Universal Laws
10 Infinite Convolutions
Higher Dimensions
Problems for Solution
Applications of Fourier Methods to Random Walks
2 Finite Intervals Walds Approximation
The WienerHopf Factorization
Implications and Applications
Two Deeper Theorems
Criteria for Persistency
Problems for Solution
Harmonic Analysis
Positive Definite Functions
Stationary Processes
Fourier Series
5 The Poisson Summation Formula
Positive Definite Sequences
L2 Theory
Stochastic Processes and Integrals
Problems for Solution
Answers to Problems
Some Books on Cognate Subjects
Index
Copyright
9788126518067
Probabilities and applied mathematics
519.2 FEL - I;Vol-II