2. Recall that the natural filtration of a discrete-time process {Xn}n≥0 is defined by F0X = {∅, Ω} and
F = σ(Χ1,..., Xn), n ≥ 1.
(a) Show that if {Xn}n≥0 is adapted to a filtration {Fn}n≥0, then F C Fn for all n ≥ 0.
(b) Show that if {Mn, Fn}n≥0 is a martingale, then {Mn, FM }n≥o is also a martingale.
