TY - JOUR
ID - 2107
TI - Conditional expectation of weak random elements
JO - Iranian Journal of Science and Technology (Sciences)
JA - IJSTS
LA - en
SN - 1028-6276
AU - Shishebor, S.
AU - Soltani, A. R.
AU - Sharifitabar, M.
AU - Sajjadnia, Z.
AD - Department of Statistics, Shiraz University, Shiraz, Iran
AD - Department of Statistics, Shiraz University (and Kuwait University) Shiraz, P.O. Box 5969 Safat 13060, Iran
AD - School of Mathematics, Institute for Research in Fundamental Sciences (IPM),
P.O. Box: 19395-5746, Tehran, Iran
Y1 - 2012
PY - 2012
VL - 36
IS - 4
SP - 461
EP - 467
KW - Pettis integral
KW - Pettis conditional expectation
KW - non-separable Banach spaces
KW - weak p-th order random
elements
DO - 10.22099/ijsts.2012.2107
N2 - We prove that the limit of a sequence of Pettis integrable bounded scalarly measurable weak random elements, of finite weak norm, with values in the dual of a non-separable Banach space is Pettis integrable. Then we provide basic properties for the Pettis conditional expectation, and prove that it is continuous. Calculus of Pettis conditional expectations in general is very different from the calculus of Bochner conditional expectations due to the lack of strong measurability and separability. In two examples, we derive the Pettis conditional expectations.
UR - http://ijsts.shirazu.ac.ir/article_2107.html
L1 - http://ijsts.shirazu.ac.ir/article_2107_c87cfa778504a93d5a67510b8340c1fa.pdf
ER -