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Perturbed Markov Chains with Damping Component
Methodology and Computing in Applied Probability ( IF 0.9 ) Pub Date : 2020-08-13 , DOI: 10.1007/s11009-020-09815-9
Dmitrii Silvestrov , Sergei Silvestrov , Benard Abola , Pitos Seleka Biganda , Christopher Engström , John Magero Mango , Godwin Kakuba

The paper is devoted to studies of regularly and singularly perturbed Markov chains with damping component. In such models, a matrix of transition probabilities is regularised by adding a special damping matrix multiplied by a small damping (perturbation) parameter ε. We perform a detailed perturbation analysis for such Markov chains, particularly, give effective upper bounds for the rate of approximation for stationary distributions of unperturbed Markov chains by stationary distributions of perturbed Markov chains with regularised matrices of transition probabilities, asymptotic expansions for approximating stationary distributions with respect to damping parameter, explicit coupling type upper bounds for the rate of convergence in ergodic theorems for n-step transition probabilities, as well as ergodic theorems in triangular array mode.



中文翻译:

具有阻尼分量的扰动马尔可夫链

本文致力于研究具有阻尼分量的规则和奇异摄动马尔可夫链。在这样的模型中,通过添加一个特殊的阻尼矩阵乘以一个小的阻尼(扰动)参数ε来对过渡概率矩阵进行正则化。我们对此类Markov链进行详细的扰动分析,尤其是通过扰动的Markov链的平稳分布,正则化的转移概率矩阵,渐近展开式近似近似的平稳分布,给出未扰动的Markov链的平稳分布的近似速率的有效上限。关于阻尼参数,n的遍历定理收敛速度的显式耦合类型上限阶跃的概率,以及三角阵列模式下的遍历定理。

更新日期:2020-08-13
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