Subcritical branching processes in random environment with immigration: survival of a single family

E. E. Dyakonova; V. A. Vatutin

Subcritical branching processes in random environment with immigration: survival of a single family

Probability 2020-09-09 v1

Authors: E. E. Dyakonova , V. A. Vatutin

Abstract

We consider a subcritical branching process in an i.i.d. random environment, in which one immigrant arrives at each generation. We consider the event $% \mathcal{A}_{i}(n)$ that all individuals alive at time $n$ are offspring of the immigrant which joined the population at time $i$ and investigate the asymptotic probability of this extreme event when $n\to\infty$ and $i$ is either fixed, or the difference $n-i$ is fixed, or $\min(i,n-i)\to\infty.$ To deduce the desired asymptotics we establish some limit theorems for random walks conditioned to be nonnegative or negative.

Keywords

code switching code-mixing sentiment classification adversarial training domain transfer learning ernie semeval-2020

Cite

@article{arxiv.2009.03672,
  title  = {Subcritical branching processes in random environment with immigration: survival of a single family},
  author = {E. E. Dyakonova and V. A. Vatutin},
  journal= {arXiv preprint arXiv:2009.03672},
  year   = {2020}
}

Comments

20 pages, 14 references. To be published in Theory of Probability and its Applications, 65(4), 2020. arXiv admin note: text overlap with arXiv:1911.00316

Subcritical branching processes in random environment with immigration: survival of a single family

Abstract

Keywords

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