Doob-Meyer decomposition of Hilbert space valued functions (Q1426855)

(1) This paper gives 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) This paper also gives a second variant of the Doob-Meyer decomposition; it is more specialized. (3) This paper applies (1) by reproving the Doléans measure in a special setting and demonstrates that the stochastic integral could be defined on more general totally ordered time scales than \(\mathbb{R}\).