Abstract For the classical Shiryaev-Roberts martingale diffusion considered on the interval where A > 0 is a given absorbing boundary, it is shown that the rate of convergence of the diffusion’s quasi-stationary cumulative distribution function (c.d.f.), to its stationary c.d.f., H(x), as is no worse than uniformly in The result is established explicitly by constructing new tight lower- and upper-bounds for using certain latest monotonicity properties of the modified Bessel K function involved in the exact closed-form formula for recently obtained by Polunchenko (2017b).

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关于 Shiryaev-Roberts 扩散准平稳分布的收敛速度

摘要 对于在 A > 0 是给定吸收边界的区间上考虑的经典 Shiryaev-Roberts 鞅扩散，表明扩散的准平稳累积分布函数 (cdf) 收敛到其平稳 cdf，H (x), as 并不比均匀更差 在最近获得的精确闭式公式中，通过使用修正贝塞尔 K 函数的某些最新单调性属性构造新的严格的上下界，明确建立结果波伦琴科 (2017b)。