V. A. Vatutin, V. A. Topchiǐ, “Catalytic branching random walks in $\mathbb Z^d$ with branching at the origin”, Mat. Tr., 14:2 (2011), 28–72; Siberian Adv. Math., 23:2 (2013), 125

Matematicheskie Trudy

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive
	Impact factor

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Mat. Tr.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Matematicheskie Trudy, 2011, Volume 14, Number 2, Pages 28–72 (Mi mt215)

This article is cited in 14 scientific papers (total in 14 papers)

Catalytic branching random walks in

$\mathbb Z^d$ with branching at the origin

V. A. Vatutin^a, V. A. Topchiĭ^b

^a Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
^b Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk, Russia

Full-text PDF (410 kB) Citations (14)

References:

PDF

HTML

Abstract: A time-continuous branching random walk on the lattice

$\mathbb Z^d$ ,

$d\ge1$ , is considered when the particles may produce offspring at the origin only. We assume that the underlying Markov random walk is homogeneous and symmetric, the process is initiated at moment

$t=0$ by a single particle located at the origin, and the average number of offspring produced at the origin is such that the corresponding branching random walk is critical. The asymptotic behavior of the survival probability of such a process at moment

$t\to\infty$ and the presence of at least one particle at the origin is studied. In addition, we obtain the asymptotic expansions for the expectation of the number of particles at the origin and prove Yaglom-type conditional limit theorems for the number of particles located at the origin and beyond at moment

$t$ .

Key words: catalytic branching random walk, a homogeneous and symmetric time-continuous multidimensional Markov random walk, Bellman–Harris branching process with two types of particles, renewal theory, limit theorem.

Received: 27.04.2010

English version:
Siberian Advances in Mathematics, 2013, Volume 23, Issue 2, Pages 125–153
DOI: https://doi.org/10.3103/S1055134413020065

Bibliographic databases:

Document Type: Article

UDC: 519.218

Language: Russian

Citation: V. A. Vatutin, V. A. Topchiǐ, “Catalytic branching random walks in

$\mathbb Z^d$ with branching at the origin”, Mat. Tr., 14:2 (2011), 28–72; Siberian Adv. Math., 23:2 (2013), 125–153

Citation in format AMSBIB

\Bibitem{VatTop11}

\by V.~A.~Vatutin, V.~A.~Topchi{\v\i}

\paper Catalytic branching random walks in~$\mathbb Z^d$ with branching at the origin

\jour Mat. Tr.

\yr 2011

\vol 14

\issue 2

\pages 28--72

\mathnet{http://mi.mathnet.ru/mt215}

\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2961768}

\elib{https://elibrary.ru/item.asp?id=17025629}

\transl

\jour Siberian Adv. Math.

\yr 2013

\vol 23

\issue 2

\pages 125--153

\crossref{https://doi.org/10.3103/S1055134413020065}

Linking options:

https://www.mathnet.ru/eng/mt215

https://www.mathnet.ru/eng/mt/v14/i2/p28

This publication is cited in the following 14 articles:

Rytova A., Yarovaya E., “Heavy-Tailed Branching Random Walks on Multidimensional Lattices. a Moment Approach”, Proc. R. Soc. Edinb. Sect. A-Math., 151:3 (2021), PII S0308210520000463, 971–992
E. Vl. Bulinskaya, “Maximum of a catalytic branching random walk”, Russian Math. Surveys, 74:3 (2019), 546–548
M. V. Platonova, K. S. Ryadovkin, “O dispersii chislennosti chastits nadkriticheskogo vetvyaschegosya sluchainogo bluzhdaniya na periodicheskikh grafakh”, Veroyatnost i statistika. 28, Zap. nauchn. sem. POMI, 486, POMI, SPb., 2019, 233–253
Ekaterina Vl. Bulinskaya, Proceedings of the 2019 2nd International Conference on Mathematics and Statistics, 2019, 6
V. A. Topchiǐ, “On renewal matrices connected with branching processes with tails of distributions of different orders”, Siberian Adv. Math., 28:2 (2018), 115–153
Bulinskaya E.V., “Strong and Weak Convergence of the Population Size in a Supercritical Catalytic Branching Process”, Dokl. Math., 92:3 (2015), 714–718
Bulinskaya E.V., “Finiteness of Hitting Times Under Taboo”, Stat. Probab. Lett., 85 (2014), 15–19
E. Vl. Bulinskaya, “Complete classification of catalytic branching processes”, Theory Probab. Appl., 59:4 (2015), 545–566
Bulinskaya E.V., “Local Particles Numbers in Critical Branching Random Walk”, J. Theor. Probab., 27:3 (2014), 878–898
V. A. Vatutin, V. A. Topchii, “Critical Bellman–Harris branching processes with long-living particles”, Proc. Steklov Inst. Math., 282 (2013), 243–272
E. Vl. Bulinskaya, “Subcritical catalytic branching random walk with finite or infinite variance of offspring number”, Proc. Steklov Inst. Math., 282 (2013), 62–72
Bulinskaya E.V., “Limit Theorems for Local Particle Numbers in Branching Random Walk”, Dokl. Math., 85:3 (2012), 403–405
E. Vl. Bulinskaya, “Hitting times with taboo for a random walk”, Siberian Adv. Math., 22:4 (2012), 227–242
V. A. Topchii, “The asymptotic behaviour of derivatives of the renewal function for distributions with infinite first moment and regularly varying tails of index $\beta\in(1/2,1]$ ”, Discrete Math. Appl., 22:3 (2012), 315–344

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	627
Full-text PDF :	190
References:	101
First page:	2

Что такое QR-код?

Registration to the website

Logotypes