Summary: Metrics on the set of semimartingale filtrations
Department of Mathematics
London SW7 2AZ
March 6, 2006
Let X be a stochastic process with cadlag paths. We consider the
set of all filtrations under which X is a semimartingale, and we define a
distance between such filtrations with the help of the bounded variation
parts in the corresponding decompositions of X. We show that this
distance is a complete metric on the set of semimartingale filtrations if
the given process X is continuous.
2000 AMS subject classifications: primary 21B28, 91B16; secondary
Key words and phrases: semimartingale; Sp; filtration; complete
metric; information drift.
Let (Ft) be a filtration on some fixed probability space satisfying the usual
conditions. The vector space of all processes which are semimartingales with