Pseudo-Regularly Varying Functions and Generalized Renewal Processes

• Main Authors: Buldygin, Valeriĭ V. (Author, http://id.loc.gov/vocabulary/relators/aut), Indlekofer, Karl-Heinz (http://id.loc.gov/vocabulary/relators/aut), Klesov, Oleg I. (http://id.loc.gov/vocabulary/relators/aut), Steinebach, Josef G. (http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Probability Theory and Stochastic Modelling, 91
• Subjects: Probabilities.; Functions of real variables.; Differential equations.; Probability Theory and Stochastic Processes.; Real Functions.; Ordinary Differential Equations.

One of the main aims of this book is to exhibit some fruitful links between renewal theory and regular variation of functions. Applications of renewal processes play a key role in actuarial and financial mathematics as well as in engineering, operations research and other fields of applied mathemati...

Table of Contents:

• Preface
• Equivalence of limit theorems for sums of random variables and renewal processes
• Almost sure convergence of renewal processes
• Generalizations of regularly varying functions
• Properties of absolutely continuous functions
• Non-degenerate groups of regular points
• Karamata's theorem for integrals
• Asymptotically quasi-inverse functions
• Generalized renewal processes
• Asymptotic behavior of solutions of stochastic differential equations
• Asymptotics for renewal processes constructed from multi-indexed random walks
• Spitzer series and regularly varying functions. - Appendix: Some Auxiliary Results
• References
• Index.