Before I state my question, I'll quote my textbook on financial derivatives:

I'm not very good at math, so this is why I'm asking this question. I thought it wasn't possible to multiply st. dev., only variance. Then why is the st. dev. of a generalized Wiener process[...] A generalized Wiener process for a variable x can be defined in terms of dz as

dx = a dt + b dz (12.3)

[...] Theb dzterm on the right-hand side of equation (12.3) can be regarded as adding noise or variability to the path followed byx.The amount of this noise or variability isbtimes a Wiener process. A Wiener process has standard deviation of 1.0. It follows thatbtimes a Wiener process has a standard deviation ofb.btimes 1.0? Thanks