1. The problem statement, all variables and given/known data How to prove that the Ito Integral int_0^t e^s dB_s is normally-distributed, for a given t? 2. Relevant equations 3. The attempt at a solution This Ito Integral could be defined as a R-S Integral, and the Riemann Sum should be a linear function of normal r.v.s, thus the Riemann Sum is normal. However I don't know how to prove that the limit of a sequence of normal random variable is normal... Or is there another way to prove it? Thanks!!