Zapiski Nauchnykh Seminarov POMI, Probability and statistics. Part 28, Tome 486 (2019), pp. 214-228
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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/
@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},
year = {2019},
volume = {486},
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
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
%U http://geodesic.mathdoc.fr/item/ZNSL_2019_486_a12/
%G ru
%F ZNSL_2019_486_a12
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 $|x|^{-2m-2}, m\in\mathbf{N}$.
