Tiexin Guo
Ekeland's Variational Principle for An $\bar{L}^{0}-$Valued Function on A Complete Random Metric Space.
Tue, 07/26/2011 - 15:01 — SomNambulAuthors: Tiexin Guo, Yujie Yang
Subjects: Functional Analysis
AbstractMotivated by the recent work on conditional risk measures, this paper studies
the Ekeland's variational principle for a proper, lower semicontinuous and
lower bounded $\bar{L}^{0}-$valued function, where $\bar{L}^{0}$ is the set of
equivalence classes of extended real-valued random variables on a probability
space. First, we prove a general form of Ekeland's variational principle for
such a function defined on a complete random metric space. Then, we give a more
precise form of Ekeland's variational principle for such a local function on a
complete random normed module.Recent progress in random metric theory and its applications to conditional risk measures.
Fri, 06/04/2010 - 15:02 — SomNambulAuthors: Tiexin Guo
Subjects: Risk Management
AbstractThe purpose of this paper is to give a selective survey on recent progress in
random metric theory and its applications to conditional risk measures.A comprehensive connection between the basic results and properties derived from two kinds of topologies for a random locally convex module.
Fri, 08/14/2009 - 21:09 — SomNambulAuthors: Tiexin Guo
Subjects: Functional Analysis
AbstractThe purpose of this paper is to make a comprehensive connection between the
basic results and properties derived from the two kinds of topologies (namely
the $(\epsilon,\lambda)-$topology introduced by the author and locally
$L^{0}-$convex topology recently introduced by Filipovi$\acute{c}$ et. al) for
a random locally convex module. First, we give an extremely simple proof of the
known Hahn-Banach extension theorem of $L^{0}-$linear functions as well as its
continuous variants. Then we give the essential relations between the
hyperplane separation theorems in [Filipovi$\acute{c}$ et.- Read more
- 7 comments
- login or register to post comments
User login
