Universal Theory for Strong Limit Theorems of Probability

This is the first book which the universal approach to strong laws of probability is discussed in. The universal theories are described for three important objects of probability theory: sums of independent random variables, processes with independent increments and renewal processes. Further generalizations are mentioned. Besides strong laws, large deviations are of independent interest. The case of infinite variations is considered as well. Readers can examine appropriate techniques and methods. Optimality of conditions is discussed.
Contents: Strong Laws and Large DeviationsLarge Deviations for Sums of Independent Random VariablesStrong Limit Theorems for Sums of Independent Random VariablesStrong Limit Theorems for Processes with Independent IncrementsStrong Limit Theorems for Renewal ProcessesIncrements of Sums of Independent Random Variables Over Head Runs and Monotone Blocks
Readership: Graduate students, researchers in Probability.Limit Theorems of Probability;Strong Laws;Sums of Independent Random Variables;Processes with Independent Increments;Renewal Processes;Functionals Over Moving Blocs;Increments of Sums of Independent Random Variables and Stochastic Processes;Strong Law of Large Numbers;Law of the Iterated Logarithm;Erdos-renyi Law;Csorgo-Revesz Law;Large Deviations00