Chapter I The Exponential and the Uniform Densities
Chapter II Special Densities. Randomization
Chapter III Densities in Higher Dimensions. Normal Densities and Processes
Chapter IV Probability Measures and Spaces
Chapter V Probability Distributions in Rr
Chapter VI A Survey of Some Important Distributions and Processes
Chapter VII Laws of Large Numbers. Applications in Analysis
Chapter VIII The Basic Limit Theorems
Chapter IX Infinitely Divisible Distributions and Semi-Groups
Chapter X Markov Processes and Semi-Groups
Chapter XI Renewal Theory
Chapter XII Random Walks in R1
Chapter XIII Laplace Transforms. Tauberian Theorems. Resolvents
Chapter XIV Applications of Laplace Transforms
Chapter XV Characteristic Functions
Chapter XVI Expansions Related to the Central Limit Theorem
Chapter XVII Infinitely Divisible Distributions
Chapter XVIII Applications of Fourier Methods to Random Walks
Chapter XIX Harmonic Analysis

An Introduction to Probability Theory and Its Applications offers comprehensive explanations to complex statistical problems. Delving deep into densities and distributions while relating critical formulas, processes and approaches, this rigorous text provides a solid grounding in probability with practice problems throughout. Heavy on application without sacrificing theory, the discussion takes the time to explain difficult topics and how to use them. This new second edition includes new material related to the substitution of probabilistic arguments for combinatorial artifices as well as new sections on branching processes, Markov chains, and the DeMoivre-Laplace theorem. --- summary provided by publisher