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Invariance principle for the critical branching process in a random environment attaining a high level. (English. Russian original) Zbl 1197.60032

Theory Probab. Appl. 54, No. 1, 1-13 (2009); translation from Teor. Veroyatn. Primen. 54, No. 1, 3-17 (2009).
Summary: A conditional invariance principle is established for the critical branching process in a random environment attaining a high level, and finite-dimensional distributions of the limiting process are found.

MSC:

60F17 Functional limit theorems; invariance principles
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60K37 Processes in random environments
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