Geodesic
On convergence of distributions for sums of independent random vectors with randomly change of components
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 269-276 
A. N. Frolov. On convergence of distributions for sums of independent random vectors with randomly change of components. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 36, Tome 535 (2024), pp. 269-276. http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a17/
@article{ZNSL_2024_535_a17,
     author = {A. N. Frolov},
     title = {On convergence of distributions for sums of independent random vectors with randomly change of components},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {269--276},
     year = {2024},
     volume = {535},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a17/}
}
TY  - JOUR
AU  - A. N. Frolov
TI  - On convergence of distributions for sums of independent random vectors with randomly change of components
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2024
SP  - 269
EP  - 276
VL  - 535
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a17/
LA  - ru
ID  - ZNSL_2024_535_a17
ER  - 
%0 Journal Article
%A A. N. Frolov
%T On convergence of distributions for sums of independent random vectors with randomly change of components
%J Zapiski Nauchnykh Seminarov POMI
%D 2024
%P 269-276
%V 535
%U http://geodesic.mathdoc.fr/item/ZNSL_2024_535_a17/
%G ru
%F ZNSL_2024_535_a17

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We derive new results on convergence of distributions for sums of independent random vectors with randomly changed components in scheme of series. In particular, a multidimensional central limit theorem is proved. If the random change of components is defined by a Poisson process then we arrive at results on convergence of finitely dimension distributions of psi-processes. In Gaussian case, the limit process is the Ornstein–Uhlenbeck process. We discuss a replacement of the Poisson process by processes with non-negative integer increments.

[1] V. Feller, Vvedenie v teoriyu veroyatnostei i ee primeneniya, v. II, Mir, 1971 | MR

[2] O. V. Rusakov, “Puassonovskie subordinatory, pole Vinera–Ornshteina–Ulenbeka i svyaz brounovskikh mostov s perekhodnymi kharakteristikami protsessov Ornshteina–Ulenbeka”, Zap. nauchn. semin. POMI, 384, 2010, 225–237

[3] O. V. Rusakov, “Psevdo-puassonovskie protsessy so stokhasticheskoi intensivnostyu i klass protsessov, obobschayuschikh protsess Ornshteina–Ulenbeka”, Vestnik SPbGU, ser. 1. Matematika, mekhanika, astronomiya, 4(62):2 (2017), 247–257 | Zbl

[4] O. V. Rusakov, A. N. Frolov, “O skhodimosti psi-protsessov k protsessam tipa Ornshteina–Ulenbeka s bezgranichno delimym raspredeleniem”, Tezisy dokladov 9-i Mezhdunarodnoi konferentsii po stokhasticheskim metodam, 2024 http://www.intconfstochmet.ru/Proceedings.html

[5] P. Embrekhts, K. Klyuppelberg, “Nekotorye aspekty strakhovoi matematiki”, Teoriya veroyatn. i ee primen., 38 (1993), 374–416

[6] A. N. Frolov, Bezgranichno delimye raspredeleniya i summy nezavisimykh sluchainykh velichin, Lan, SPb, 2023