Asymptotic Analysis of Random Walks: Heavy-Tailed Distributions

Introduction 1. Preliminaries 2. Random walks with jumps having no finite first moment 3. Random walks with finite mean and infinite variance 4. Random walks with jumps having finite variance 5. Random walks with semiexponential jump distributions 6. Random walks with exponentially decaying distributions 7. Asymptotic properties of functions of distributions 8. On the asymptotics of the first hitting times 9. Large deviation theorems for sums of random vectors 10. Large deviations in the space of trajectories 11. Large deviations of sums of random variables of two types 12. Non-identically distributed jumps with infinite second moments 13. Non-identically distributed jumps with finite variances 14. Random walks with dependent jumps 15. Extension to processes with independent increments 16. Extensions to generalised renewal processes Bibliographic notes Index of notations Bibliography.