Geodesic
Limit theorems on convergence to generalized Cauchy type processes
Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 214-228

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

We prove a limit theorem on convergence of mathematical expectations of functionals of sums of independent random variables to a Cauchy problem solution for an evolution equation $\frac{\partial{u}}{\partial{t}}=(-1)^m\mathcal{A}_mu$ where $\mathcal{A}_m$ is a convolution operator with a generalized function $|x|^{-2m-2}, m\in\mathbf{N}$. 
@article{ZNSL_2019_486_a12,
     author = {A. K. Nikolaev and M. V. Platonova},
     title = {Limit theorems on convergence to generalized {Cauchy} type processes},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {214--228},
     publisher = {mathdoc},
     volume = {486},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a12/}
}
TY  - JOUR
AU  - A. K. Nikolaev
AU  - M. V. Platonova
TI  - Limit theorems on convergence to generalized Cauchy type processes
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2019
SP  - 214
EP  - 228
VL  - 486
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a12/
LA  - ru
ID  - ZNSL_2019_486_a12
ER  - 
%0 Journal Article
%A A. K. Nikolaev
%A M. V. Platonova
%T Limit theorems on convergence to generalized Cauchy type processes
%J Zapiski Nauchnykh Seminarov POMI
%D 2019
%P 214-228
%V 486
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a12/
%G ru
%F ZNSL_2019_486_a12
A. K. Nikolaev; M. V. Platonova. Limit theorems on convergence to generalized Cauchy type processes. Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 214-228. http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a12/