Abstract:
We consider a supercritical symmetric continuous-time branching random walk
on a multidimensional lattice with a finite number of particle generation
sources of varying positive intensities without any restrictions on the
variance of jumps of the underlying random walk. It is assumed that the
spectrum of the evolution operator contains at least one positive
eigenvalue. We prove that under these conditions the largest eigenvalue of
the evolution operator is simple and determines the rate of exponential
growth of particle quantities at each point on the lattice as well as on
the lattice as a whole.
Keywords:
branching random walk, multiple sources, supercritical case, limit theorem, particle number exponential growth.
Citation:
I. Khristolyubov, E. B. Yarovaya, “A limit theorem for supercritical random branching walks with branching sources of varying intensity”, Teor. Veroyatnost. i Primenen., 64:3 (2019), 456–480; Theory Probab. Appl., 64:3 (2019), 365–384
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\by I.~Khristolyubov, E.~B.~Yarovaya
\paper A limit theorem for supercritical random branching walks with branching sources of varying intensity
\jour Teor. Veroyatnost. i Primenen.
\yr 2019
\vol 64
\issue 3
\pages 456--480
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\transl
\jour Theory Probab. Appl.
\yr 2019
\vol 64
\issue 3
\pages 365--384
\crossref{https://doi.org/10.1137/S0040585X97T989556}
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Linking options:
https://www.mathnet.ru/eng/tvp5245
https://doi.org/10.4213/tvp5245
https://www.mathnet.ru/eng/tvp/v64/i3/p456
This publication is cited in the following 15 articles:
M. V. Platonova, K. S. Ryadovkin, “Vetvyaschiesya diffuzionnye protsessy v periodicheskikh sredakh”, Veroyatnost i statistika. 36, Zap. nauchn. sem. POMI, 535, POMI, SPb., 2024, 214–236
M. V. Platonova, K. S. Ryadovkin, “Moment asymptotics of particle numbers at vertices for a supercritical branching random walk on a periodic graph”, Theory Probab. Appl., 68:2 (2023), 231–249
E. Filichkina, E. Yarovaya, “Branching random walks with one particle generation center and possible absorption at every point”, Mathematics, 11:7 (2023), 1676
V. Kutsenko, E. Yarovaya, “Symmetric branching random walks in random media: comparing theoretical and numerical results”, Stochastic Models, 39:1 (2023), 60
N. V. Smorodina, E. B. Yarovaya, “Martingale method for studying branching random walks”, Russian Math. Surveys, 77:5 (2022), 955–957
Rytova A., Yarovaya E., “Survival Analysis of Particle Populations in Branching Random Walks”, Commun. Stat.-Simul. Comput., 50:10 (2021), 3031–3045
A. Rytova, E. Yarovaya, “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
M. V. Platonova, K. S. Ryadovkin, “On the Variance of the Particle Number of a Supercritical Branching Random Walk on Periodic Graphs”, J Math Sci, 258:6 (2021), 897
Elena Chernousova, Yaqin Feng, Ostap Hryniv, Stanislav Molchanov, Joseph Whitmeyer, “Steady states of lattice population models with immigration”, Mathematical Population Studies, 28:2 (2021), 63
Elena Yarovaya, Daria Balashova, Ivan Khristolyubov, Springer Proceedings in Mathematics & Statistics, 371, Recent Developments in Stochastic Methods and Applications, 2021, 144
“Abstracts of talks given at the 4th International Conference on Stochastic Methods”, Theory Probab. Appl., 65:1 (2020), 121–172
E. Vl. Bulinskaya, “On the maximal displacement of catalytic branching random walk”, Sib. elektron. matem. izv., 17 (2020), 1088–1099
A. I. Rytova, E. B. Yarovaya, “Moments of the numbers of particles in a heavy-tailed branching random walk”, Russian Math. Surveys, 74:6 (2019), 1126–1128
E. B. Yarovaya, J. Stoyanov, K. K. Kostyashin, “On conditions for a probability distribution to be uniquely determined by its moments”, Theory Probab. Appl., 64:4 (2020), 579–594
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
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