I need a little help with a problem. I am given some stochastic processes and supposed to show that they are $\mathcal{F_t}-$martingales. The first one is this, and they all look similar:
$$X_t=e^{t/2} \cdot \cos{W_t}.$$
Is this different from showing that it is a martingale? And how can and shall I use Itô's formula here:
For some $f(t,x)$, $$f(t,W_t)=f(0,0)+\int_0^t\frac{\partial f}{\partial x}(s,W_s)dW_s+\int_0^{t}\frac{\partial f}{\partial t}(s,W_s)ds + \frac{1}{2}\int_0^t\frac{\partial^2f}{\partial x^2}(s,W_s)ds.$$
Thanks for your help!
Marie :*