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Principle Seminar of the Department of Probability Theory, Moscow State University
November 9, 2011 16:45, Moscow, MSU, auditorium 16-24
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Bellman-Harris processes and their
application to branching random walks
E. Vl. Bulinskaya
M. V. Lomonosov Moscow State University
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Abstract:
In the talk, we consider critical catalytic branching random walk on
an integer lattice having an arbitrary starting point. The main
attention is paid to finding the asymptotic behavior of the
probability of the particles presence at an arbitrary fixed point of
the lattice as time tends to infinity. Moreover, the Yaglom type
conditional limit theorems are established for the number of
particles at each point of the lattice. The method of proof is based
on introduction of an auxiliary Bellman-Harris branching process
with particles of six types. An essential role is played by the
proposed notion of "a hitting time with taboo" for a
(non-branching) random walk on the lattice.
[1] Bulinskaya E.Vl. Limit Theorems for Local Particles
Numbers in Branching Random Walk. Doklady RAN (in print).
[2] Bulinskaya E.Vl. The Hitting Times with Taboo for a Random
Walk on an Integer Lattice. Prepublication de LPMA UPMC
no.1456 (2011), 25 pp.; arXiv:1107.1074v1 [math.PR].
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