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- W1981136113 abstract "Consider a reversible (self-adjoint) Markov process with a discrete time parameter and stationary transition probability functions satisfying the Harris recurrence condition. $mathbf{P}^{(n)}(x, S)$ denotes the $n$-step transition probability function from $x$ to the measurable set $S$ and $pi$ is the sigma-finite stationary measure induced by the above hypotheses. Using both a functional analytic representation for reversible probabilities and probabilistic identities, various limits are considered for both general and discrete spaces. The principle result gives necessary and sufficient conditions for sets $A$ and $mathbf{B}$ so that a reversible, aperiodic Markov process satisfies the strong ratio limit property $lim_{mrightarrowinfty} mathbf{P}^{(n + k)} (mu, mathbf{A})/mathbf{P}^{(n)} (nu, mathbf{B}) = pi(mathbf{A})/pi(mathbf{B}$ where $mu$ and v are arbitrary probability distributions defined on the space and $k$ is any integer." @default.
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- W1981136113 date "1973-12-01" @default.
- W1981136113 modified "2023-10-14" @default.
- W1981136113 title "Limit Theorems for Reversible Markov Processes" @default.
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- W1981136113 doi "https://doi.org/10.1214/aop/1176996807" @default.
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