Could someone help me with this:
Let be Brownian motion and .Prove that is Brownian motion.
Check that the process satisfies the characteristic properties of Brownian motion: , is Gaussian with mean 0 and variance , has stationary independent increments, and is almost surely continuous (maybe you know another characterization of B.M. from your lecture; then adapt the sentence). All of these properties are immediate consequences of the same properties for .