Pseudo-Regularly Varying Functions and Generalized Renewal Processes. 1st ed. 2018

種類:

電子ブック

責任表示:

by Valeriĭ V. Buldygin, Karl-Heinz Indlekofer, Oleg I. Klesov, Josef G. Steinebach

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Buldygin, Valeriĭ V.
• Indlekofer, Karl-Heinz.
• Klesov, Oleg I.
• Steinebach, Josef G.
• SpringerLink (Online service)

シリーズ名:

Probability Theory and Stochastic Modelling ; 91

ISBN:

9783319995373 [3319995375]    

注記:

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.
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 mathematics. On the other hand, regular variation of functions is a property that features prominently in many fields of mathematics. The structure of the book reflects the historical development of the authors’ research work and approach – first some applications are discussed, after which a basic theory is created, and finally further applications are provided. The authors present a generalized and unified approach to the asymptotic behavior of renewal processes, involving cases of dependent inter-arrival times. This method works for other important functionals as well, such as first and last exit times or sojourn times (also under dependencies), and it can be used to solve several other problems. For example, various app

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