The state x(t) of a geometric Brownian motion satisfies an Ito differential equation:
d x(t) = μ * x(t) dt + σ*x(t) dw(t), where w(t) follows a standard Wiener Process.
The state of x(t) follows a LogNormal Distribution of [(μ-) t+ Log[x0]]
The parameter μ can be any real number, and σ and x0...