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Author Delbaen, F. ♦ Schachermayer, W.
Source CiteSeerX
Content type Text
Publisher Birkhauser
File Format PDF
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Singular Part ♦ Bounded Variation ♦ New Proof ♦ Compactness Theorem ♦ Optional Decomposition Theorem ♦ Roughly Speaking ♦ Bounded Sequence ♦ Kadec-pe Czynski-decomposition ♦ General Case ♦ Weakly Compact ♦ Semi-martingale Topology ♦ Compactness Principle ♦ Mathematical Finance
Description For H¹ bounded sequences, we introduce a technique, related to the Kadec-Pełczynski-decomposition for L¹ sequences, that allows us to prove compactness theorems. Roughly speaking, a bounded sequence in H¹ can be split into two sequences, one of which is weakly compact, the other forms the singular part. If the martingales are continuous then the singular part tends to zero in the semi-martingale topology. In the general case the singular parts give rise to a process of bounded variation. The technique allows to give a new proof of the optional decomposition theorem in Mathematical Finance.
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Article
Publisher Date 1996-01-01
Publisher Institution PROCEEDINGS OF THE SEMINAR OF STOCHASTIC ANALYSIS, RANDOM FIELDS AND APPLICATIONS, PROGRESS IN PROBABILITY