Pseudo-Regularly Varying Functions and Generalized Renewal Processes

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...

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Bibliographic Details
Main Author: Buldygin, Valeriĭ V. (Author)
Format: Electronic eBook
Language:English
Published: Cham : Springer International Publishing, 2018.
Edition:1st ed. 2018.
Series:Probability Theory and Stochastic Modelling, 91
Subjects:
Probabilities.
Functions of real variables.
Differential equations.
ISBN:9783319995373
ISSN:2199-3130 ;
Online Access: Get full text
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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.

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