设φ为状态空间在[0,∞)上齐次离散时间马尔可夫链φm,为φ的m-骨架.Meyn与Tweedie在文献[1]中以1-骨架为条件研究了马氏链收敛速度的界.本文将弱化该条件,以m-骨架(m≥1)代替1-骨架,计算出马氏链中的几何收敛速度的界,从而推广了[1]中的成果.
Assuming that φ is a time-homogeneous discrete-time Markov chains with m-skeleton φm on the state space [0, ∞). Meyn and Tweedie have studied the bounds on convergence rates of Markov chains φ with conditions of 1-skeleton in the literature [1]. This paper is an attempt to weaken those conditions, that is, it manages to change 1-skeleton into m-skeleton .At the same time,it calculates the bounds on geometric convergence rates of Markov chains φ with weak conditions of m-skeleton(m≥1 ) in order to generalize the result of [1].