Abstract: The investigated processes ~(t), 0~t<~, may be interpreted as the population size of particles at time t, each of themdeveloping independently from the behavior of the remaining particles. The process starts at time zero with one particle and the evolution of the individual particles is defined by a family of independent, identically distributed processes {N, N(t)}, where N defines the lifetime of a particle, while N(t) is the total number of descendants of a particle of age t (the time passed from the moment of its birth). We mention that in the random process {~, N(t)} no restrictions are assumed on the dependence between ~ and the finite collections N(ti), i.e., no relation form is ruled out between the moments of the birth of the descendants, their number, and the lifetimes of the parents. A more detailed description of the process can be found in [i] or [2]; moreover, the construction and the description of the probability space from [2] are used here in an essential manner.

Cite: Topchy V.A.
Properties of the nonextinction probability of general critical branching processes under weak constrainis
Siberian Mathematical Journal. 1987. V.28. N5. P.832–845. DOI: 10.1007/BF00969331 Scopus РИНЦ OpenAlex

Original: Топчий В.А.
Свойства вероятности продолжения общих критических ветвящихся процессов при слабых ограничениях
Сибирский математический журнал. 1987. Т.28. №5. 5 :1-15. DOI: 10.1137%2F1127083 РИНЦ

Dates:

Submitted:	Mar 21, 1985
Published print:	Sep 1, 1987

Identifiers:

≡ Scopus:	2-s2.0-34250096802
≡ Elibrary:	46550203
≡ OpenAlex:	W2048534126

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