Part of the Stochastic Modelling and Applied Probability book series (SMAP, volume 13)
Let L denote the family of all real-valued functions Y t (ω) defined on R + × Ω which are measurable with respect to ℬ(R +) × A and have the following properties:
Y = (Y t ) is adapted to (G t ).
For each ω,the function t → Y t (ω) is left-continuous.
KeywordsSimple Process Finite Interval Quadratic Variation Continuous Version Stochastic Integral
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- Section 3.1 is based on the ideas of Dellacherie  and Courrège . The proofs of the theorems stated in 3.1 are to be found in . The process ((4) of Theorem 3.1.4 is called the dual predictable projection of (Ut) by Dellacherie . Section 3.2 is based on Meyer [43, 44] and Courrège . A full discussion of Ito’s stochastic integral is given in Ito . Lemma 3.3.1 is from Gihman and Skorohod . Lemma 3.3.3 is given in Friedman .Google Scholar
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