Orthogonality, Stable Subspaces and Covariation Processes in Enlargement of Filtration
In this talk we discuss about the covariation process [X, Y ] of two orthogonal local martingales X and Y , its structure and its relationship with the stable subspaces generated by X and Y . In particular, when not trivial, [X, Y ] cannot belong to the stable subspace generated by the pair (X, Y ). This result reflects on the growth of Jacod’s dimension in the setting of enlargement of filtration arising when X and Y are a F-local martingale enjoying the F-predictable representation property and a H-local martingale enjoying the H-predictable representation property, respectively. More precisely, denoting by G the filtration F∨H, when X and Y are orthogonal G-local martingales and [X, Y ] is non-zero, previous result applies to show that the Jacod dimension of G is exactly three. This talk is based on a joint work with Antonella Calzolari.
Area: IS9 - Martingale representations and enlargement of filtrations (Claudio Fontana)
Keywords: Martingale representation, enlargement of filtrations
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