关于起始于拟平稳分布的非负马尔可夫过程的首次退出时间的期望
On the Expectation of the First Exit Time of a Nonnegative Markov Process Started at a Quasistationary Distribution
摘要：
设{M_n}_{\ge 0} $ be a nonnegative Markov process with stationary transition probabilities. The quasistationary distributions referred to in this note are of the form Q_A(x) = lim_{n\to\infty} P(M_n \le x | M_0 \le A, M_1 \le A, ..., M_n \le A) . Suppose that $ M_0 $ has distribution $ \Qb_A $ and define T_A^{Q_A} = \min\{n | M_n > A, n\ge 1\}, the first time when M_n exceeds A. We provide sufficient conditions for E T_A^{Q_A}$是A的一个增函数.
英文摘要：
Let {M_n}_{n\ge 0}$ be a nonnegative Markov process with stationary transition probabilities. The quasistationary distributions referred to in this note are of the form Q_A(x) = lim_{n\to\infty} P(M_n \le x | M_0 \le A, M_1 \le A, ..., M_n \le A) . Suppose that $M_0$ has distribution $\Qb_A$ and define T_A^{Q_A} = \min\{n | M_n > A, n\ge 1\}, the first time when M_n exceeds A. We provide sufficient conditions for E T_A^{Q_A}$ to be an increasing function of A.
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