8V - Geometric Brownian motion

[Bill the Catuary]

Question:

Is it ever the case that a(x,t) and b(x,t) are actually functions of BOTH x and t, and not just x where variable x follows GBM??

i.e.,

if dx = mu*x dt + sigma*x dz,

then the drift rate, a, is mu*x
and the variance rate, b^2, is (sigma*x)^2

Both a and b are functions of x only. Are they ever also functions of t if variable x follows GBM?

thanks!