Path properties of the primitives of a Brownian motion

Authors
Lin, ZY
Citation
Zy. Lin, Path properties of the primitives of a Brownian motion, J AUS MAT A, 70, 2001, pp. 119-133
Citations number
7
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS
ISSN journal
02636115 → ACNP
Volume
70
Year of publication
2001
Part
1
Pages
119 - 133
Database
ISI
SICI code
0263-6115(200102)70:<119:PPOTPO>2.0.ZU;2-D
Abstract
Let {W(t), t greater than or equal to 0} be a standard Brownian motion. For a positive integer m, define a Gaussian process X-m(t) = 1/m! integral (t)(0) (t - s)(m) dW(s). Watanabe and Lachal gave some asymptotic properties of the process X-m(.), m greater than or equal to 1. In this paper, we study the bounds of its mod uli of continuity and large increments by establishing large deviation resu lts.