TY - JOUR
T1 - Regularity of local times of random fields
AU - Ren, Jiagang
AU - Zhang, Xicheng
PY - 2007/8/1
Y1 - 2007/8/1
N2 - In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales.
AB - In this paper, we study the fractional smoothness of local times of general processes starting from the occupation time formula, and obtain the quasi-sure existence of local times in the sense of the Malliavin calculus. This general result is then applied to the local times of N-parameter d-dimensional Brownian motions, fractional Brownian motions and the self-intersection local time of the 2-dimensional Brownian motion, as well as smooth semimartingales.
KW - Fractional Brownian motion
KW - Local time
KW - N-Parameter d-dimensional Brownian motion
KW - Quasi-sure existence
KW - Self-intersection local time
KW - Smooth semimartingale
UR - http://www.scopus.com/inward/record.url?scp=34250635572&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2007.04.017
DO - 10.1016/j.jfa.2007.04.017
M3 - Article
AN - SCOPUS:34250635572
SN - 0022-1236
VL - 249
SP - 199
EP - 219
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -