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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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