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 Deviations
Large Deviations for Sums of Independent Random Variables
Strong Limit Theorems for Sums of Independent Random Variables
Strong Limit Theorems for Processes with Independent Increments
Strong Limit Theorems for Renewal Processes
Increments of Sums of Independent Random Variables Over Head Runs and Monotone Blocks


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