TY - JOUR
T1 - A bounded property for gradients of diffusion semigroups on Euclidean spaces
AU - Liang, Song
N1 - Copyright:
Copyright 2004 Elsevier B.V., All rights reserved.
PY - 2004/11/1
Y1 - 2004/11/1
N2 - We consider uniformly elliptic diffusion processes X(t,x) on Euclidean spaces Rd, with some conditions in terms of the drift term (see assumptions A2 and A3). By using interpolation theory, we show a bounded property which gives an estimate of ∇xE[f(X(t,x))] involving |x| and ||f||∞ but not ||∇f||∞, and a power of 1/t smaller than 1.
AB - We consider uniformly elliptic diffusion processes X(t,x) on Euclidean spaces Rd, with some conditions in terms of the drift term (see assumptions A2 and A3). By using interpolation theory, we show a bounded property which gives an estimate of ∇xE[f(X(t,x))] involving |x| and ||f||∞ but not ||∇f||∞, and a power of 1/t smaller than 1.
KW - Diffusion
KW - Euclidean space
KW - Gradient
KW - Interpolation theory
UR - http://www.scopus.com/inward/record.url?scp=4344597560&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=4344597560&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2003.11.001
DO - 10.1016/j.jfa.2003.11.001
M3 - Article
AN - SCOPUS:4344597560
SN - 0022-1236
VL - 216
SP - 71
EP - 85
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
IS - 1
ER -