Electronic Communications in Probability

Some conditional limiting theorems for symmetric Markov processes with tightness property

Guoman He, Ge Yang, and Yixia Zhu

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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.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 60, 11 pp.

Received: 3 January 2019
Accepted: 16 September 2019
First available in Project Euclid: 1 October 2019

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Primary: 60J25: Continuous-time Markov processes on general state spaces
Secondary: 37A30: Ergodic theorems, spectral theory, Markov operators {For operator ergodic theory, see mainly 47A35} 60J60: Diffusion processes [See also 58J65]

symmetric Markov process conditional ergodic theorem quasi-stationary distribution one-dimensional diffusions intrinsic ultracontractivity

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He, Guoman; Yang, Ge; Zhu, Yixia. Some conditional limiting theorems for symmetric Markov processes with tightness property. Electron. Commun. Probab. 24 (2019), paper no. 60, 11 pp. doi:10.1214/19-ECP265. https://projecteuclid.org/euclid.ecp/1569895735

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