Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform
Abstract
:1. Preliminary
1.1. Infinitely Divisible Distribution
1.2. Related Distribution Classes
1.3. Esscher Transform
2. Main Results
3. The Proofs of Theorems 1–3
3.1. Proof of Theorem 1
3.2. Proof of Theorem 2
3.3. Proof of Theorem 3
4. On the Condition (10)
5. Conclusions and Future Work
5.1. Theoretical Significance and Application Value
5.2. On the Embrechts–Goldie Conjecture
5.3. Some Unresolved Problems
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Cui, Z.; Wang, Y.; Xu, H. Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform. Mathematics 2022, 10, 4128. https://doi.org/10.3390/math10214128
Cui Z, Wang Y, Xu H. Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform. Mathematics. 2022; 10(21):4128. https://doi.org/10.3390/math10214128
Chicago/Turabian StyleCui, Zhaolei, Yuebao Wang, and Hui Xu. 2022. "Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform" Mathematics 10, no. 21: 4128. https://doi.org/10.3390/math10214128
APA StyleCui, Z., Wang, Y., & Xu, H. (2022). Local Closure under Infinitely Divisible Distribution Roots and Esscher Transform. Mathematics, 10(21), 4128. https://doi.org/10.3390/math10214128