ABSTRACT
F∞ = σ(⋃n≥0Fn).F∞ is a σ -algebra that is going to play an important role. Definition 3.1 A real adapted process (Xn)n≥0 is a martingale (resp. a supermartingale, a submartingale ) if it is integrable and if, for every n ∈ N,
E(Xn+1 |Fn) = Xn a.s. (resp. ≤,≥).
