Periodic branching random walk on $\mathbf {Z}^d$ with immigration
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 90-108 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

We consider a continuous-time branching random walk with immigration on $\mathbf {Z}^d$ with branching sources located periodically. The asymptotic behavior of the mean number of particles at an arbitrary point is obtained for $t\to\infty$ in the supercritical and subcritical cases.
@article{ZNSL_2023_526_a5,
     author = {I. I. Lukashova},
     title = {Periodic branching random walk on $\mathbf {Z}^d$ with immigration},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {90--108},
     year = {2023},
     volume = {526},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a5/}
}
TY  - JOUR
AU  - I. I. Lukashova
TI  - Periodic branching random walk on $\mathbf {Z}^d$ with immigration
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2023
SP  - 90
EP  - 108
VL  - 526
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a5/
LA  - ru
ID  - ZNSL_2023_526_a5
ER  - 
%0 Journal Article
%A I. I. Lukashova
%T Periodic branching random walk on $\mathbf {Z}^d$ with immigration
%J Zapiski Nauchnykh Seminarov POMI
%D 2023
%P 90-108
%V 526
%U http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a5/
%G ru
%F ZNSL_2023_526_a5
I. I. Lukashova. Periodic branching random walk on $\mathbf {Z}^d$ with immigration. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 35, Tome 526 (2023), pp. 90-108. http://geodesic.mathdoc.fr/item/ZNSL_2023_526_a5/

[1] B. A. Sevastyanov, Vetvyaschiesya protsessy, Nauka, M., 1971

[2] M. Cranston, L. Koralov, S. Molchanov, B. Vainberg, “A solvable model for homopolymers and self-similarity near the critical point”, Rand. Oper. Stoch. Eq., 18:1 (2010), 73–95 | MR | Zbl

[3] M. Kimmel, D. E. Axelrod, Branching Processes in Biology, Springer, 2002 | MR | Zbl

[4] C. R. Nelson, C. R. Plosser, “Trends and random walks in macroeconomic time series: some evidence and implications”, J. Monetary Econom., 10:2 (1982), 139–162 | DOI

[5] B. G. Malkiel, K. McCue, A random walk down Wall Street, Norton, New York, 1985

[6] E. A. Antonenko, E. B. Yarovaya, “Raspolozhenie polozhitelnykh sobstvennykh znachenii v spektre evolyutsionnogo operatora v vetvyaschemsya sluchainom bluzhdanii”, Sovremennye problemy matem. i mekhan., X:3 (2015), 9–22

[7] E. B. Yarovaya, Vetvyaschiesya sluchainye bluzhdaniya v neodnorodnoi srede, TsPI pri mekhmate Mosk. un-ta, M., 2007, 104 pp.

[8] E. B. Yarovaya, “Kriterii eksponentsialnogo rosta chisla chastits v modelyakh vetvyaschikhsya sluchainykh bluzhdanii”, Teoriya veroyatn. i ee primen., 55:4 (2010), 705–731 | DOI

[9] K. B. Athreya, P. E. Ney, Branching Processes, Courier Corporation, 2004 | MR

[10] E. B. Yarovaya, “Spektralnye svoistva evolyutsionnykh operatorov v modelyakh vetvyaschikhsya sluchainykh bluzhdanii”, Matem. zametki, 92:1 (2012), 123–140 | DOI | Zbl

[11] M. V. Platonova, K. S. Ryadovkin, “Asimptoticheskoe povedenie srednego chisla chastits vetvyaschegosya sluchainogo bluzhdaniya na reshetke $\mathbf{Z}^d$ s periodicheskimi istochnikami vetvleniya”, Zap. nauchn. semin. POMI, 466, 2017, 234–256

[12] M. V. Platonova, K. S. Ryadovkin, “O srednem chisle chastits vetvyaschegosya sluchainogo bluzhdaniya na reshetke s periodicheskimi istochnikami vetvleniya”, Dokl. Akad. nauk, 479:3 (2018), 250–253 | DOI | Zbl

[13] M. V. Platonova, K. S. Ryadovkin, “Vetvyaschiesya sluchainye bluzhdaniya na $\mathbf{Z}^d$ s periodicheski raspolozhennymi istochnikami vetvleniya”, Teoriya veroyatn. i ee primen., 64:2 (2019), 283–307 | DOI | MR | Zbl

[14] D. Han, Yu. Makarova, S. Molchanov, E. Yarovaya, Branching Random Walks with Immigration, Analyt. Comput. Methods Probab. Theory, 2017 | MR | Zbl

[15] B. Mohar, “Some relations between analytic and geometric properties of infinite graphs”, Discrete Math., 95:1 (1991), 193–219 | DOI | MR | Zbl

[16] M. Reed, B. Simon, IV: Analysis of Operators, Elsevier, 1978 | MR

[17] B. A. Sevastyanov, “Predelnye teoremy dlya vetvyaschikhsya sluchainykh protsessov spetsialnogo vida”, Teoriya veroyatn. i ee primen., 2:3 (1957), 339–348 | Zbl

[18] M. Sh. Birman, M. Z. Solomyak, Spektralnaya teoriya samosopryazhennykh operatorov v gilbertovom prostranstve, Lan, 2022

[19] F. P. Gantmakher, Teoriya matrits, Nauka, M., 1966 | MR

[20] M. V. Fedoryuk, Metod perevala, Nauka, M., 1977