Time does the process spend in state

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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?

Reference no: EM131130627

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