Kozlov, M. V. A conditional function limit theorem for a critical branching process in a random medium. (English. Russian original) Zbl 0884.60085 Dokl. Math. 52, No. 2, 164-167 (1995); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 1, 12-15 (1995). There are established a conditional function limit theorem for the Wilkinson-Smith branching processes under the condition that it is nondegenerate on the time interval \([0,n]\) and \(n\to \infty\). The results are connected with B. Durret’s one [Ann. Probab. 6, 798-828 (1978; Zbl 0398.60023)]. This is the main part for the proof scheme connections of the process with some random walk and special constructed Markov chain. Reviewer: V.Topchij (Omsk) Cited in 1 ReviewCited in 2 Documents MSC: 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) 60F17 Functional limit theorems; invariance principles 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 60G50 Sums of independent random variables; random walks 60J85 Applications of branching processes Keywords:measure-valued branching processes; random walk; Markov chain; Wilkinson-Smith processes; invariance principle Citations:Zbl 0398.60023 PDFBibTeX XMLCite \textit{M. V. Kozlov}, Dokl. Math. 52, No. 2, 164--167 (1995; Zbl 0884.60085); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 344, No. 1, 12--15 (1995)