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Some conditional limiting theorems for symmetric Markov processes with tightness property. (English) Zbl 1423.60117
Summary: Let \(X\) be an \(\mu \)-symmetric irreducible Markov process on \(I\) with strong Feller property. In addition, we assume that \(X\) possesses a tightness property. In this paper, we prove some conditional limiting theorems for the process \(X\). The emphasis is on conditional ergodic theorem. These results are also discussed in the framework of one-dimensional diffusions.
MSC:
60J25 Continuous-time Markov processes on general state spaces
37A30 Ergodic theorems, spectral theory, Markov operators
47A35 Ergodic theory of linear operators
60J60 Diffusion processes
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