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
5 - Integro-Local Limit Theorems under the Cramér Moment Condition
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 continue the study of integro-local probabilities that was initiated in Chapter 2 in the normal deviation zone. Now, assuming that the vector (?, ?) satisfies the Cramér moment condition, we study the integro-local probability in a wider zone, which in analogy with random walks can be called the Cramér deviation zone. This zone includes the zones of normal, moderately large, and "usual" large deviations.
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- Chapter
- Information
- Compound Renewal Processes , pp. 225 - 274Publisher: Cambridge University PressPrint publication year: 2022