Predictable extensions of given filtrations

• Autorzy: Dettweiler E.
• Języki publikacji: EN

Abstrakty

EN

Filtrations with the property that every stopping time is predictable are of some importance in stochastic analysis, especially in connection with the Girsanov transformation (cf. e.g. Chung and Williams [1]). Presumably for that reason, S. Kwapień stated the problem whether any given filtration can be extended (in a sense defined below) to a filtration for which every stopping time is predictable. In this paper, this problem of Kwapień is solved positively: Any filtration has a predictable extension. The extension we construct has even the stronger property: any square integrable martingale is a stochastic integral process relative to a certain Brownian motion.

Słowa kluczowe

EN

stochastic analysis; ntegrable martingale; Brownian motion

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2001
• Tom: Vol. 21, Fasc. 2
• Strony: 351--370
• Opis fizyczny: Bibliogr. 3 poz.

Twórcy

autor

Dettweiler E.

• Mathematisches Institut der Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany

Bibliografia

• [1] K. L, Chung and R. X Williams, Introduction to Stochastic Integration, 2nd edition, Birkhäüser, Boston 1990.
• [2] I. Kara Izas and St. E. Shreve, Brownian Motion and Stochastic Calculus, Springer, New York 1988.
• [3] M. Metivier, Semimartingales, W. de Gruyter, Berlin 1982.