With the aid of Taylor series expansion(also called Itos Lemma in stochastic calculus),which of the following stochastic processes are martingales under the real world probability measure P where Wt is a Brownian motion:

With the aid of Taylor series expansion (also called Ito's Lemma in stochastic calculus), which of the following stochastic processes are martingales under the real world probability mea- sure P where W, is a Brownian motion: 1. X(t) = 20.5t cos(W+). 2. X(t) = 0.5t sin(Wt). 3. X(t) = (W++t) .exp(-W+ - 0.5t). With the aid of Taylor series expansion (also called Ito's Lemma in stochastic calculus), which of the following stochastic processes are martingales under the real world probability mea- sure P where W, is a Brownian motion: 1. X(t) = 20.5t cos(W+). 2. X(t) = 0.5t sin(Wt). 3. X(t) = (W++t) .exp(-W+ - 0.5t)