Geodesic
Harmonic analysis of random walks with heavy tails
Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 175-189.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a continuous-time symmetric, spatially homogeneous branching random walk on a multidimensional lattice with a single branching source. Corresponding transition intensities of the underlying random walk are assumed to have heavy tails. This assumption implies that the variance of jumps is infinite. The growth rate estimate of the Fourier transform for transition intensities and of the asymptotics of the mean number of particles in the source in subcritical case are obtained. 
@article{FPM_2020_23_1_a9,
     author = {A. I. Rytova},
     title = {Harmonic analysis of random walks with heavy tails},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {175--189},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a9/}
}
TY  - JOUR
AU  - A. I. Rytova
TI  - Harmonic analysis of random walks with heavy tails
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2020
SP  - 175
EP  - 189
VL  - 23
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a9/
LA  - ru
ID  - FPM_2020_23_1_a9
ER  - 
%0 Journal Article
%A A. I. Rytova
%T Harmonic analysis of random walks with heavy tails
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2020
%P 175-189
%V 23
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a9/
%G ru
%F FPM_2020_23_1_a9
A. I. Rytova. Harmonic analysis of random walks with heavy tails. Fundamentalʹnaâ i prikladnaâ matematika, Tome 23 (2020) no. 1, pp. 175-189. http://geodesic.mathdoc.fr/item/FPM_2020_23_1_a9/

[1] Rytova A. I., Yarovaya E. B., “Mnogomernaya lemma Vatsona i ee primenenie”, Matem. zametki, 99:3 (2016), 395–403 | MR | Zbl

[2] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1, 2, Mir, M., 1984 | MR

[3] Yarovaya E. B., Vetvyaschiesya sluchainye bluzhdaniya v neodnorodnoi srede, Tsentr prikl. issled. pri mekhaniko-matematicheskom f-te MGU, M., 2007

[4] Yarovaya E. B., “Spektralnaya asimptotika nadkriticheskogo vetvyaschegosya sluchainogo bluzhdaniya”, Teoriya veroyatn. i ee primen., 62:3 (2017), 518–541

[5] Agbor A., Molchanov S., Vainberg B., “Global limit theorems on the convergence of multidimensional random walks to stable processes”, Stoch. Dyn., 15:3 (2015), 1550024 | DOI | MR | Zbl

[6] Albeverio S., Bogachev L. V., Yarovaya E. B., “Asymptotics of branching symmetric random walk on the lattice with a single source”, C. R. Acad. Sci. Paris. Sér. I, Math., 326 (1998), 975–980 | DOI | MR | Zbl

[7] Borovkov A., Borovkov K., Asymptotic Analysis of Random Walks. Heavy-Tailed Distributions, Cambridge Univ. Press, Cambridge, 2008 | MR | Zbl

[8] Kozyakin V., “Hardy type asymptotics for cosine series in several variables with decreasing power-like coefficients”, Int. J. Adv. Res. Math., 5 (2016), 35–51 | DOI

[9] Vatutin V. A., Topchii V. A., “Limit theorem for critical catalytic branching random walks”, Theory Probab. Appl., 49:3 (2005), 498–518 | DOI | MR | Zbl

[10] Yarovaya E. B., “Use of spectral methods to study branching processes with diffusion in a noncompact phase space”, Theor. Math. Phys., 88:1 (1991), 690–694 | DOI | MR | Zbl

[11] Yarovaya E., “Branching random walks with heavy tails”, Commun. Statist. Theory Methods, 42:16 (2013), 2301–2310 | DOI | MR

[12] Yarovaya E., “Criteria for transient behavior of symmetric branching random walks on $\mathbb{Z}$ and $\mathbb{Z}^2$”, New Perspectives on Stochastic Modeling and Data Analysis, eds. J. R. Bozeman, V. Girardin, C. H. Skiadas, ISAST, 2014, 283–294

[13] Yarovaya E. B., “The structure of the positive discrete spectrum of the evolution operator arising in branching random walks”, Dokl. Math., 92:1 (2015), 507–510 | DOI | MR | Zbl