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May 8, 2023 at 23:23 comment added Fabrice Baudoin The "therefore" follows from Girsanov theorem, but essentially if P(<X>_T <+\infty)=0 for one process then it should also be zero for the other process since the laws of the two processes are equivalent on the time interval [0,T]
May 8, 2023 at 22:26 comment added El_mago Many thanks for your answer and drawing my attention to this interesting paper about the equivalence of Volterra processes! I have to think about your "therefore". In particular, is it clear that two continuous processes that are locally equivalent are neither both a semimartingale nor both not a semimartingale?
May 8, 2023 at 1:46 history answered Fabrice Baudoin CC BY-SA 4.0