Pseudo-regularly varying functions and generalized renewal processes. ([2018])

• Record Type: Book
• Further Information: Note: Valeriĭ V. Buldygin, Karl-Heinz Indlekofer, Oleg I. Klesov and Josef G. Steinebach.
• Authors: Buldygin, V. V (Valeriĭ Vladimirovich); Indlekofer, Karl-Heinz; Klesov, Oleg; Steinebach, Josef G
• Contents: Intro; Preface; Acknowledgements; Contents; 1 Equivalence of Limit Theorems for Sums of Random Variables and Renewal Processes; 1.1 Introduction; 1.2 Strong Limit Theorems for Partial Sums; 1.3 Renewal Processes with Linear Drift; 1.3.1 Results; 1.3.2 Proofs; 1.4 Renewal Processes Without Linear Drift; 1.4.1 Results; 1.4.2 Proofs; 1.5 Comments; 2 Almost Sure Convergence of Renewal Processes; 2.1 Introduction; 2.2 Almost Sure Limit Theorems; 2.2.1 The Strong Law of Large Numbers; 2.2.2 Non-equivalent Strong Laws; 2.2.3 Rate of Convergence; 2.3 Examples 2.3.1 Renewal Processes Constructed from Independent, Identically Distributed Random Variables2.3.2 Nonidentically Distributed or Dependent Interarrival Times; 2.4 Comments; 3 Generalizations of Regularly Varying Functions; 3.1 Introduction; 3.2 RV- and ORV-Functions; 3.2.1 Some Notation; 3.2.2 Upper and Lower Limit Functions; 3.2.3 RV- and SV-Functions; 3.2.4 ORV- and OSV-Functions; 3.2.5 OURV-Functions; 3.3 Four Important Classes of Functions; 3.3.1 PRV-Functions; 3.3.1.1 Some Simple Properties of WPRV- and PRV-Functions; 3.3.2 PI- and SQI-Functions 3.3.2.1 Some Simple Properties of WSQI- and SQI-Functions3.3.3 POV-Functions; 3.3.3.1 Some Simple Properties of POV-Functions; 3.4 Functions Preserving the Asymptotic Equivalence; 3.4.1 A Uniform Convergence Theorem; 3.4.2 A Uniform Convergence Theorem for SV- and RV-Functions; 3.5 Integral Representations; 3.5.1 Integral Representations for RV- and ORV-Functions; 3.5.2 Integral Representations for PRV-Functions; 3.5.3 Integral Representations for POV-Functions; 3.6 Potter's Bounds for PRV-Functions; 3.7 Convergence to Infinity of PI-Functions; 3.7.1 A Counterexample 4.4.3 A Characterization of Properties of Absolutely Continuous Functions4.4.4 Admissible Transformations of Densities; 4.5 Elasticity and Indices of Asymptotic Elasticity; 4.5.1 Elasticity of Functions; 4.5.2 Indices of Asymptotic Elasticity; 4.5.3 Essential Indices of Asymptotic Elasticity; 4.5.4 Examples; 4.5.5 Arithmetic Properties of Indices of Asymptotic Elasticity; 4.6 Relationships in Terms of the Indices of AsymptoticElasticity; 4.7 Functions with Bounded Asymptotic Elasticity; 4.7.1 Admissible Transformations of Densities; 4.7.2 The ER-Property of Absolutely ContinuousFunctions
• Publisher Details: Cham : Springer
• Publication Date: 2018
• Copyright Date: 2018
• Extent: 1 online resource
• Subjects: 519.2; Mathematics; Renewal theory; Functions; Distribution (Probability theory); Differential Equations; MATHEMATICS / Applied; MATHEMATICS / Probability & Statistics / General; Mathematics -- Mathematical Analysis; Mathematics -- Differential Equations; Real analysis, real variables; Differential calculus & equations; Mathematics -- Probability & Statistics -- General; Probability & statistics; Electronic books
• Languages: English
• ISBNs: 9783319995373; 3319995375
• Related ISBNs: 9783319995366
• Notes: Note: Includes bibliographical references and index.; Note: Online resource ; title from PDF title page (EBSCO, viewed October 17, 2018).
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.