Doob–Meyer-Decomposition of Hilbert Space Valued Functions

B. Burgstaller ()
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B. Burgstaller: University Linz

Journal of Theoretical Probability, 2003, vol. 16, issue 4, 877-898

Abstract: Abstract (1) We give here a new proof of the Doob–Meyer-decomposition which is rather quick and elementary. It is more general in some aspects, and weaker in other aspects if compared to other approaches. The functions are defined on a totally ordered set with image in a Hilbert space. (2) We also give a second variant of the Doob–Meyer-decomposition; it is more specialized. (3) We apply (1) by reproving the Doléans-measure in a special setting and demonstrate that the stochastic integral could be defined on more general totally ordered time scales then $$\mathbb{R}$$ .

Keywords: Doob–Meyer; decomposition; Hilbert space; totally ordered set; Doleans measure; stochastic integral (search for similar items in EconPapers)
Date: 2003
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DOI: 10.1023/B:JOTP.0000011998.44302.3b

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