Abstract:
In a model of a supercritical catalytic branching random walk (CBRW) on the integers $\mathbb {Z}$, the case of light tails of the walk jump is considered, i.e., the Cramér condition is imposed. A limit theorem in the sense of almost sure convergence is proved for the first time of hitting a linearly growing (in time) high level by particles. In the limit, there arises the same constant as in the limit theorem for the maximum of a CBRW.
Keywords:catalytic branching random walk, supercritical regime, propagation front, Cramér condition, first hitting time.
Citation:
E. Vl. Bulinskaya, “First Hitting Time of a High Level by a Catalytic Branching Walk”, Branching Processes and Related Topics, Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin, Trudy Mat. Inst. Steklova, 316, Steklov Math. Inst., Moscow, 2022, 105–112; Proc. Steklov Inst. Math., 316 (2022), 97–104
\Bibitem{Bul22}
\by E.~Vl.~Bulinskaya
\paper First Hitting Time of a High Level by a Catalytic Branching Walk
\inbook Branching Processes and Related Topics
\bookinfo Collected papers. On the occasion of the 75th birthday of Andrei Mikhailovich Zubkov and 70th birthday of Vladimir Alekseevich Vatutin
\serial Trudy Mat. Inst. Steklova
\yr 2022
\vol 316
\pages 105--112
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4211}
\crossref{https://doi.org/10.4213/tm4211}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2022
\vol 316
\pages 97--104
\crossref{https://doi.org/10.1134/S0081543822010084}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129127404}
Citation in format AMSBIB
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