Abstract
The usual setup for the general theory of processes is a complete probability space (Ω,ℱ,ℙ) endowed with a filtration (ℱ t )t ≥0: each ℱtis a sub-σ-field of ℱ, contains all negligible events in ℱand ℱ t =∩ε>0 ℱ t+ε ; this equality says that t↦ℱ t is increasing and right-continuous. Increasingness is the main point; the other conditions are mere technical assumptions. Removing them is possible, but rarely useful, and makes some results heavier.
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© 1989 Springer-Verlag Berlin Heidelberg
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Emery, M. (1989). Real semimartingales and stochastic integrals. In: Stochastic Calculus in Manifolds. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-75051-9_1
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DOI: https://doi.org/10.1007/978-3-642-75051-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-51664-4
Online ISBN: 978-3-642-75051-9
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