TY - BOOK AU - Feller, William TI - An Introduction to Probability :Theory and its Applications Vol - ll SN - 9788126518067 U1 - 519.2 FEL - I;Vol-II PY - 1971/// CY - New Delhi PB - Wiley India KW - Probabilities and applied mathematics N1 - 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 UR - https://books.google.co.in/books?id=OXkg-LvRgjUC&printsec=frontcover&dq=Introduction+to+Probability+Theory+and+its+Applications+Vol+-+ll&hl=en&sa=X&ved=0ahUKEwiI-raqo5TnAhUUVH0KHecrAJcQ6AEIKDAA#v=onepage&q=Introduction%20to%20Probability%20Theory%20and%20its%20Applications%20Vol%20-%20ll&f=false ER -