TY - JOUR
T1 - Relatively compact families of functionals on abstract Wiener space and applications
AU - Zhang, Xicheng
PY - 2006/3/1
Y1 - 2006/3/1
N2 - In this paper we prove two relatively compact criterions in some Lp-spaces(p > 1) for the set of functionals on abstract Wiener space in terms of the compact embedding theorems in finite dimensional Sobolev spaces. Then, as applications we study several relatively compact families of random fields for the solutions to SDEs (and SPDEs) with coefficients satisfying some bounded assumptions, some stochastic integrals, and local times of diffusion processes.
AB - In this paper we prove two relatively compact criterions in some Lp-spaces(p > 1) for the set of functionals on abstract Wiener space in terms of the compact embedding theorems in finite dimensional Sobolev spaces. Then, as applications we study several relatively compact families of random fields for the solutions to SDEs (and SPDEs) with coefficients satisfying some bounded assumptions, some stochastic integrals, and local times of diffusion processes.
KW - Malliavin calculus
KW - Relatively compact criterion
KW - Stochastic differential equation
KW - Stochastic partial differential equation
KW - Wiener-Sobolev space
UR - https://www.scopus.com/pages/publications/31144458860
U2 - 10.1016/j.jfa.2005.06.016
DO - 10.1016/j.jfa.2005.06.016
M3 - Article
AN - SCOPUS:31144458860
SN - 0022-1236
VL - 232
SP - 195
EP - 221
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -