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Recent progress in random metric theory and its applications to conditional risk measures
The purpose of this paper is to give a selective survey on recent progress in
random metric theory and its applications to conditional risk measures. This
paper includes eight sections. Section 1 is a longer introduction, which gives
a brief introduction to random metric theory, risk measures and conditional
risk measures. Section 2 gives the central framework in random metric theory,
topological structures, important examples, the notions of a random conjugate
space and the Hahn-Banach theorems for random linear functionals. Section 3
gives several important representation theorems for random conjugate spaces.
Section 4 gives characterizations for a complete random normed module to be
random reflexive. Section 5 gives hyperplane separation theorems currently
available in random locally convex modules. Section 6 gives the theory of
random duality with respect to the locally convex topology and in
particular a characterization for a locally convex module to be
prebarreled. Section 7 gives some basic results on convex
analysis together with some applications to conditional risk measures. Finally,
Section 8 is devoted to extensions of conditional convex risk measures, which
shows that every representable type of conditional convex risk
measure and every continuous type of convex conditional risk measure
() can be extended to an type
of lower semicontinuous conditional convex risk measure and an
type of continuous
conditional convex risk measure (), respectively.Comment: 37 page
Iterative Detection of Diagonal Block Space Time Trellis Codes, TCM and Reversible Variable Length Codes for Transmission over Rayleigh Fading Channels
Iterative detection of Diagonal Block Space Time Trellis Codes (DBSTTCs), Trellis Coded Modulation (TCM) and Reversible Variable Length Codes (RVLCs) is proposed. With the aid of efficient iterative decoding, the proposed scheme is capable of providing full transmit diversity and a near channel capacity performance. The performance of the proposed scheme was evaluated when communicating over uncorrelated Rayleigh fading channels. Explicitly, significant iteration gains were achieved by the proposed scheme, which was capable of performing within 2~dB from the channel capacity
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