Geodesic
First Hitting Time of a High Level by a Catalytic Branching Walk
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 105-112

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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, Cramér condition, first hitting time.
Mots-clés : propagation front 
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     author = {E. Vl. Bulinskaya},
     title = {First {Hitting} {Time} of a {High} {Level} by a {Catalytic} {Branching} {Walk}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {105--112},
     publisher = {mathdoc},
     volume = {316},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2022_316_a7/}
}
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E. Vl. Bulinskaya. First Hitting Time of a High Level by a Catalytic Branching Walk. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Branching Processes and Related Topics, Tome 316 (2022), pp. 105-112. http://geodesic.mathdoc.fr/item/TM_2022_316_a7/