Let {B{t), t ≥ 0} be a standard Brownian motion, that is, a Wiener process with drift coefficient 𝜇 = 0 and diffusion coefficient σ2 = 1. Suppose that when B(t) = a {> 0) or b = -α, the process spends an exponential time with parameter λ = 2 in this state (α or b = -α). Then, it starts again from state 0.
(a) What fraction of time does the process spend in state α or b = -α, over a long period?
