期刊
PROBABILITY THEORY AND RELATED FIELDS
卷 158, 期 1-2, 页码 55-89出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s00440-012-0477-5
关键词
Markov process; Potential theory; Non-reversible; Dirichlet principle; Recurrence
We extend the Dirichlet principle to non-reversible Markov processes on countable state spaces. We present two variational formulas for the solution of the Poisson equation or, equivalently, for the capacity between two disjoint sets. As an application we prove a some recurrence theorems. In particular, we show the recurrence of two-dimensional cycle random walks under a second moment condition on the winding numbers.
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