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

This article is cited in 2 scientific papers (total in 2 papers)

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
Received: 01.12.2011

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
    Related articles on Google Scholar: Russian articles, English articles

    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  crossref  mathscinet  zmath  isi  elib  scopus
    2. E. Vl. Bulinskaya, “Complete classification of catalytic branching processes”, Theory Probab. Appl., 59:4 (2015), 545–566  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математические труды Siberian Advances in Mathematics
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