Book contents
- Frontmatter
- Contents
- Introduction
- 1 Main Limit Laws in the Normal Deviation Zone
- 2 Integro-Local Limit Theorems in the Normal Deviation Zone
- 3 Large Deviation Principles for Compound Renewal Processes
- 4 Large Deviation Principles for Trajectories of Compound Renewal Processes
- 5 Integro-Local Limit Theorems under the Cramér Moment Condition
- 6 Exact Asymptotics in Boundary Crossing Problems for Compound Renewal Processes
- 7 Extension of the Invariance Principle to the Zones of Moderately Large and Small Deviations
- Appendix A On Boundary Crossing Problems for Compound Renewal Processes when the Cramér Condition Is Not Fulfilled
- Basic Notation
- References
- Index of Special Symbols
Appendix A - On Boundary Crossing Problems for Compound Renewal Processes when the Cramér Condition Is Not Fulfilled
Published online by Cambridge University Press: 16 June 2022
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Book contents
- Frontmatter
- Contents
- Introduction
- 1 Main Limit Laws in the Normal Deviation Zone
- 2 Integro-Local Limit Theorems in the Normal Deviation Zone
- 3 Large Deviation Principles for Compound Renewal Processes
- 4 Large Deviation Principles for Trajectories of Compound Renewal Processes
- 5 Integro-Local Limit Theorems under the Cramér Moment Condition
- 6 Exact Asymptotics in Boundary Crossing Problems for Compound Renewal Processes
- 7 Extension of the Invariance Principle to the Zones of Moderately Large and Small Deviations
- Appendix A On Boundary Crossing Problems for Compound Renewal Processes when the Cramér Condition Is Not Fulfilled
- Basic Notation
- References
- Index of Special Symbols
Summary
For the case where the jump distributions vary regularly at infinity (slow decay), for the sake of completeness we present without proof a number of results from A. A. Borovkov and K. A. Borovkov,Asymptotic Analysis of Random Walks. Vol. I: Slowly Decaying Jump Distributions (in Russian; Moscow: Fizmatlit, 2008).
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- Chapter
- Information
- Compound Renewal Processes , pp. 341 - 351Publisher: Cambridge University PressPrint publication year: 2022