Some potential theorems for countable transient jump processes

Zhi-Sheng Tong, Zhi-Wen Cheng, Xiu-Fang Liu and Ying-Chuan Jing

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 10, 2980-2989

Abstract: This article extends the potential theory to countable transient jump processes based on the works of Kemeny, Snell, and Knapp (1976) and Syski (1979). First, it presents the construction of excessive measures. Using excessive measures, this article defines elementary concepts in potential theory. Thus most conclusions for Markov chains can be generalized to jump processes. One of the most important results is the variational formulas for the energy of equilibrium potentials, which holds for asymmetric processes.

Date: 2025
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DOI: 10.1080/03610926.2024.2379036

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