We prove that certain jump summation processes converge in distribution for the uniform topology to the Brownian sheet, while smoothed summation processes converge for various Lipschitz topologies. These results follow after a careful study of abstract, generalized Lipschitz spaces. Along the way we affirm a conjecture about smoothness and continuity of processes defined on $\lbrack 0, 1\rbrack^d$.
Publié le : 1981-10-14
Classification:
Lipschitz spaces,
weak convergence,
central limit theorem,
summation processes,
60B10,
60G17,
60G50
@article{1176994311,
author = {Erickson, Roy V.},
title = {Lipschitz Smoothness and Convergence with Applications to the Central Limit Theorem for Summation Processes},
journal = {Ann. Probab.},
volume = {9},
number = {6},
year = {1981},
pages = { 831-851},
language = {en},
url = {http://dml.mathdoc.fr/item/1176994311}
}
Erickson, Roy V. Lipschitz Smoothness and Convergence with Applications to the Central Limit Theorem for Summation Processes. Ann. Probab., Tome 9 (1981) no. 6, pp. 831-851. http://gdmltest.u-ga.fr/item/1176994311/