I have a standard brownian motion under probability measure $\displaystyle P$, let $\displaystyle Z(t)$ be the exponential martingale $\displaystyle Z(t)=exp{-thetaB(t)-1/2(theta)^2t}$. Define measure $\displaystyle Q(A)=E[Z(t)1a]$ as a probability measure. I need to show that the process $\displaystyle Xt=Bt+theta*t$ (Brownian motion with drift) is a standard brownian motion under measure $\displaystyle Q$ WITHOUT using C-M or Girsanov theorems, but instead using Levy's characterisation of brownian motion to show that under $\displaystyle Q$, $\displaystyle Xt$ is a cont. martingale.

I am pulling my hear out on this one!!