Local Functional Limit Theorems of Increments for Brownian Motion

Authors
Gao, Fu Qing Liu, Yong Hong
Citation
Gao, Fu Qing et Liu, Yong Hong, Local Functional Limit Theorems of Increments for Brownian Motion, Acta mathematica Sinica. English series (Print) , 34(7), 2018, pp. 1074-1086
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
34
Issue
7
Year of publication
2018
Pages
1074 - 1086
Database
ACNP
SICI code
Abstract
In this paper, we present a local Csörgö.Révész type functional limit theorem for increments of Brownian motion and give its convergence rate. The results also extend the functional forms of Lévy.s modulus of continuity for Brownian motion.