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
2 - Integro-Local Limit Theorems in the Normal Deviation Zone
Published online by Cambridge University Press: 16 June 2022
- 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 prove several results about the asymptotics of the distributions of nonnormalized CRPs Z(t) and Y(t). These results, known as integro-local theorems, are sharper than the central limit theorem and are concerned with the probabilities of Z(t) and Y(t) hitting intervals of small length in the normal deviation zone.
- Type
- Chapter
- Information
- Compound Renewal Processes , pp. 57 - 89Publisher: Cambridge University PressPrint publication year: 2022