New Limit Theorems for Increments of Birth-and-Death Processes with Linear Rates
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Bibliographic record
Abstract
We investigate the short-term temporal evolution of the classical birth-and-death process with linear birth and death rates.We prove weak convergence of its increments to those of the Skellam process in the Skorohod space.Similar convergence results are established under a different set of assumptions on the model parameters and the time horizon.We also discuss related short-term approximations in terms of Skellam distributions for the marginals of such birth-and-death processes which start from a growing number of particles.For two special cases of the pure birth and pure death processes, our results yield those on weak convergence to the corresponding Poisson processes.
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Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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