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Random walks and branching processes. (Случайные блуждания и ветвящиеся процессы.) (Russian) Zbl 1304.60001
Lektsionnye Kursy NOTs 6. Moskva: Matematicheskiĭ Institut im. V. A. Steklova, RAN (ISBN 5-98419-018-4/pbk). 187 p. (2007).
This book presents a series of lectures, read by V. I. Afanasyev during the 2005/2006 academic year, to students of Moscow universities. Along with classical presentations of random walk theory and the theory of branching processes, the lectures also reflect the results of joint research of German mathematicians and mathematicians of the Steklov Mathematical Institute. The relationship of branching processes in a random environment and conditional random walks is observed. Among the topics covered are: the invariance principle of Donsker-Prokhorov, conditional invariance principle of Liggett, conditional invariance principle of Iglehart, identities of Sparre Andersen and Spitzer, Galton-Watson processes, and branching processes in a random environment.
The author also points out connections between branching processes in a random environment and conditional random walks.
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60G40 Stopping times; optimal stopping problems; gambling theory
60K37 Processes in random environments
60J65 Brownian motion
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