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 Mat. Tr., 2012, Volume 15, Number 1, Pages 3–26 (Mi mt222)

Hitting times with taboo for a random walk

E. Vl. Bulinskaya

Lomonosov Moscow State University, Moscow, Russia

Abstract: For a symmetric homogeneous and irreducible random walk on the $d$-dimensional integer lattice, which have a finite variance of jumps, we study passage times (taking values in $[0,\infty]$) determined by a starting point $x$, a hitting state $y$, and a taboo state $z$. We find the probability that these passage times are finite, and study the distribution tail. In particular, it turns out that, for the above-mentioned random walks on $\mathbb Z^d$ except for a simple random walk on $\mathbb Z$, the order of the distribution tail decrease is specified by dimension $d$ only. In contrast, for a simple random walk on $\mathbb Z$, the asymptotic properties of hitting times with taboo essentially depend on mutual location of the points $x,y$, and $z$. These problems originated in recent study of a branching random walk on $\mathbb Z^d$ with a single source of branching.

Key words: random walk on integer lattice, hitting time, taboo probability, branching random walk.

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English version:
Siberian Advances in Mathematics, 2012, 22:4, 227–242

Bibliographic databases:

UDC: 519.21

Citation: E. Vl. Bulinskaya, “Hitting times with taboo for a random walk”, Mat. Tr., 15:1 (2012), 3–26; Siberian Adv. Math., 22:4 (2012), 227–242

Citation in format AMSBIB
\Bibitem{Bul12} \by E.~Vl.~Bulinskaya \paper Hitting times with taboo for a~random walk \jour Mat. Tr. \yr 2012 \vol 15 \issue 1 \pages 3--26 \mathnet{http://mi.mathnet.ru/mt222} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2984673} \elib{http://elibrary.ru/item.asp?id=17718095} \transl \jour Siberian Adv. Math. \yr 2012 \vol 22 \issue 4 \pages 227--242 \crossref{https://doi.org/10.3103/S1055134412040013} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Bulinskaya E.V., “Finiteness of Hitting Times Under Taboo”, Stat. Probab. Lett., 85 (2014), 15–19
2. E. Vl. Bulinskaya, “Complete classification of catalytic branching processes”, Theory Probab. Appl., 59:4 (2015), 545–566
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