Quickest detection of a hidden target and extremal surfaces

Abstract

Let Z = (Zt)t≥0 be a regular diffusion process started at 0, let ℓ be an independent random variable with a strictly increasing and continuous distribution function F, and let τℓ = inf { t ≥ 0 | Zt = ℓ} be the first entry time of Z at the level ℓ. We show that the quickest detection problem inf P(τ <τℓ) + c E(τ −τℓ)

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