=+where > 0 and 0 are constants so that 1

=+where σ > 0 and 0 ≤ μ are constants so that 1 − μ − σ ≥ 0, ξn are i.i.d.

random variables with the law P(ξn = ±1) = 1/2 and S0 > 0. Prove that Sn is a supermartingale. For which μ is it a martingale?