马尔科夫链中群逆稳定性分析

Sensitivity Analysis of Group Inverse in Markov Chains

令P是有限状态离散马尔科夫链的转移矩阵,群逆(I-P)#在马尔科夫链分析中有着重要应用.给出了当P的每一个元素有小的相对扰动时,(I-P)#在范数意义下的相对扰动误差界.所得的界只依赖于矩阵的阶数,而与马尔科夫链本身的性质无关.

Let P be the transition matrix of a discrete-time Markov chain. The group inverse （I-P）# plays an important role in the analysis of the Markov chain. It＇s analyzed that the sensitivity of group inverse under the entrywise perturbation in P. The error bound shows that the sensitivity is independent of the condition of the Markov chain.