Probabilistic approximation of a Riemann–Liouville type operator with a stability index greater than two
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 5-27 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper, we introduce Riemann-Liouville type operators for the complex index $\alpha$. A probabilistic approximation of the solution of the Cauchy problem for an evolutionary equation with a Riemann–Liouville type operator for a complex $\alpha$ is constructed.
@article{ZNSL_2022_510_a0,
     author = {I. A. Alekseev},
     title = {Probabilistic approximation of a {Riemann{\textendash}Liouville} type operator with a stability index greater than two},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--27},
     year = {2022},
     volume = {510},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a0/}
}
TY  - JOUR
AU  - I. A. Alekseev
TI  - Probabilistic approximation of a Riemann–Liouville type operator with a stability index greater than two
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2022
SP  - 5
EP  - 27
VL  - 510
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a0/
LA  - ru
ID  - ZNSL_2022_510_a0
ER  - 
%0 Journal Article
%A I. A. Alekseev
%T Probabilistic approximation of a Riemann–Liouville type operator with a stability index greater than two
%J Zapiski Nauchnykh Seminarov POMI
%D 2022
%P 5-27
%V 510
%U http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a0/
%G ru
%F ZNSL_2022_510_a0
I. A. Alekseev. Probabilistic approximation of a Riemann–Liouville type operator with a stability index greater than two. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 32, Tome 510 (2022), pp. 5-27. http://geodesic.mathdoc.fr/item/ZNSL_2022_510_a0/

[1] I. A. Alekseev, “Ustoichivye sluchainye velichiny s kompleksnym indeksom ustoichivosti, II”, Teoriya veroyatnostei i ee primeneniya (to appear)

[2] T. Kato, Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972 | MR

[3] M. V. Platonova, “Veroyatnostnoe predstavlenie resheniya zadachi Koshi dlya evolyutsionnogo uravneniya s operatorom Rimana-Liuvillya”, Teoriya veroyatn. i ee primen., 61:3 (2013), 417–438

[4] A. V. Skorokhod, Sluchainye protsessy s nezavisimymi prirascheniyami, Nauka, M., 1964

[5] K. Sato, Lévy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 2013 | MR