You are given the representation:
Where the equality holds given the sequence of information sets {It. The underlying process Xt is known to follow the SDE:
dXt = μdt + σdWt
Determine the g(-) in the above representation for the case where M(-) is given by:
(a) MT(XT) = WT
(b) MT(XT) = W2T
(c) MT(XT) =EWT