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
1 - Main Limit Laws in the Normal Deviation Zone
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
We present the basic limit theorems for CRPs in the domain of normal deviations (with the functional limit theorems), including the case of infinite variance of the jumps of the process. We also present the law of the iterated logarithm and its analogs.
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- Compound Renewal Processes , pp. 1 - 56Publisher: Cambridge University PressPrint publication year: 2022