I have a standard brownian motion under probability measure , let be the exponential martingale . Define measure as a probability measure. I need to show that the process (Brownian motion with drift) is a standard brownian motion under measure WITHOUT using C-M or Girsanov theorems, but instead using Levy's characterisation of brownian motion to show that under , is a cont. martingale.
I am pulling my hear out on this one!!