On the Expectation of the First Exit Time of a Nonnegative Markov Process Started at a Quasistationary Distribution

الأصل · EN

Let Mₙₙ≥ ₀ be a nonnegative Markov process with stationary transition probabilities. The quasistationary distributions referred to in this note are of the form Qₐ(x) = limₙ→∞ P(Mₙ ≤ x | M₀ ≤ A, M₁ ≤ A,..., Mₙ ≤ A). Suppose that M₀ has distribution ₐ and define TₐQᵃ = {n | Mₙ > A, n≥ 1}, the first time when Mₙ exceeds A. We provide sufficient conditions for E TₐQᵃ to be an increasing function of A.