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On Seneta–Heyde scaling for a stable branching random walk
| Content Provider | Scilit |
|---|---|
| Author | He, Hui Liu, Jingning Zhang, Mei |
| Copyright Year | 2018 |
| Description | We consider a discrete-time branching random walk in the boundary case, where the associated random walk is in the domain of attraction of an α-stable law with 1 < α < 2. We prove that the derivative martingale $D_{n}$ converges to a nontrivial limit $D_{∞}$ under some regular conditions. We also study the additive martingale $W_{n}$ and prove that n^{1/α}$W_{n}$ converges in probability to a constant multiple of $D_{∞}$. |
| Related Links | http://arxiv.org/pdf/1610.03575 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/53212E3FF7F5C36BE2048F875F717017/S0001867818000253a.pdf/div-class-title-on-seneta-heyde-scaling-for-a-stable-branching-random-walk-div.pdf |
| Ending Page | 599 |
| Page Count | 35 |
| Starting Page | 565 |
| ISSN | 00018678 |
| e-ISSN | 14756064 |
| DOI | 10.1017/apr.2018.25 |
| Journal | Advances in Applied Probability |
| Issue Number | 2 |
| Volume Number | 50 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2018-06-01 |
| Access Restriction | Open |
| Subject Keyword | Advances in Applied Probability Branching Random Walk Domain of Attraction Seneta–hedye Scaling Stable Distribution Derivative Martingale Additive Martingale Primary 60j80 Secondary 60f05 |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics Statistics and Probability |
