4 papers · 1 filter
Potentials of skip-free Markov chains
Wendi Li, Jinpeng Liu, Yuanyuan Liu
Potential theory has important applications in various fields such as physics, finance, and biology. In this paper, we investigate the potentials of two classic types of discrete-t…
Hoeffding's inequality for continuous-time Markov chains
Jinpeng Liu, Yuanyuan Liu, Lin Zhou
Hoeffding's inequality is a fundamental tool widely applied in probability theory, statistics, and machine learning. In this paper, we establish Hoeffding's inequalities specifical…
Matrix-analytic methods for solving Poisson's equation with applications to Markov chains of GI/G/1-type
Jinpeng Liu, Yuanyuan Liu, Yiqiang Q. Zhao
In this paper, we are devoted to developing matrix-analytic methods for solving Poisson's equation for irreducible and positive recurrent discrete-time Markov chains (DTMCs). Two s…
Augmented truncation approximations to the solution of Poisson's equation for Markov chains
Jinpeng Liu, Yuanyuan Liu, Yiqiang Q. Zhao
Poisson's equation has a lot of applications in various areas. Usually it is hard to derive the explicit expression of the solution of Poisson's equation for a Markov chain on an i…