Universal Theory for Strong Limit Theorems of Probability

Contents
Preface
Acronyms
1. Strong Laws and Large Deviations
	1.1 Strong Limit Theorems of Probability Theory: Results, Problems and Methods
	1.2 The Universal Strong Laws and the Large Deviations Method
2. Large Deviations for Sums of Independent Random Variables
	2.1 Probabilities of Large Deviations
	2.2 The Method of Conjugate Distributions
	2.3 Completely Asymmetric Stable Laws with Exponent α >1
	2.4 Functions of Large Deviations Theory and a Classification
of Probability Distributions
	2.5 Large Deviations and a Non-Invariance
	2.6 Methods of Conjugate Distributions and Truncations
	2.7 Asymptotic Expansions of Functions of Large Deviations
Theory in Case of Finite Variations
	2.8 Large Deviations in Case of Finite Variations
	2.9 Asymptotic Expansions of Functions of Large Deviations
Theory for D(2)
	2.10 Asymptotic Expansions of Functions of Large Deviations
Theory for DN(α) and D(α)
	2.11 Large Deviations for D(2)
	2.12 Large Deviations for DN(α) and D(α)
	2.13 Large Deviations and the Classification of Distributions
	2.14 Bibliographical Notes
3. Strong Limit Theorems for Sums of Independent Random Variables
	3.1 Norming Sequences in Strong Limit Theorems
	3.2 Universal Strong Laws in Case of Finite Exponential
Moments
	3.3 Universal Strong Laws for Random Variables without
Exponential Moment
	3.4 Corollaries of the Universal Strong Laws
		3.4.1 The Erdos–Renyi and Shepp Laws
		3.4.2 The Csorgo–Revesz Laws
		3.4.3 The Law of the Iterated Logarithm
		3.4.4 The Strong Law of Large Numbers
		3.4.5 Results for Moduli of Increments of Sums of Independent
Random Variables
	3.5 Optimality of Moment Assumptions
	3.6 Necessary and Sufficient Conditions for the Csorgo–Revesz Laws
	3.7 Bibliographical Notes
4. Strong Limit Theorems for Processes with Independent Increments
	4.1 The Universal Strong Laws for Processes with Independent
Increments
	4.2 Strong Laws for Increments of Wiener and Stable
Processes without Positive Jumps
	4.3 Applications of the Universal Strong Laws
	4.4 Compound Poisson Processes
	4.5 Bibliographical Notes
5. Strong Limit Theorems for Renewal Processes
	5.1 The universal Strong Laws for Renewal Processes
	5.2 Corollaries of the Universal Strong Laws
	5.3 Bibliographical Notes
6. Increments of Sums of Independent Random Variables over Head Runs and Monotone Blocks
	6.1 Head Runs and Monotone Blocks
	6.2 Increments of Sums over Head Runs and Monotone
Blocks
	6.3 The Universal Strong Laws
	6.4 Corollaries of the Universal Strong Laws
	6.5 Bibliographical Notes
Bibliography
Author Index
General Index