Hi,

I've to prove that a couple of equations are martingales. yet i don't really know where to start (well i know that if i can show them as driftless or as an itos integral that would answer the questions.)

I was hoping someone could give me suggestions on where to start - rather than simply answer the questions (i do want to learn it)

note i've used | to mean integral from 0 to t

and X(t) is the Brownian Motion

the equations are:

Y(t) = [1 - X(t)|sin(kX(t)).dk ] * e^(t/2)

Y(t) = sqrt(t)X(t) - | X(s)/2sqrt(s).ds

Y(t) = wX_{1}(t) + sqrt(1-w^2)*X_{2}(t)

I think I have to integrate equations 1 and 2 (in respect to k and s) but i'm getting into a muddle. Any suggestions?