## Martingale approximations for continuous-time and discrete-time stationary Markov processes.(English)Zbl 1073.60050

Summary: We show that the method of C. Kipnis and S. R. S. Varadhan [Commun. Math. Phys. 104, 1–19 (1986; Zbl 0588.60058)] to construct a martingale approximation to an additive functional of a stationary ergodic Markov process via the resolvent is universal in the sense that a martingale approximation exists if and only if the resolvent representation converges. A sufficient condition for the existence of a martingale approximation is also given. As examples we discuss moving average processes and processes with normal generator.

### MSC:

 60G44 Martingales with continuous parameter 60F05 Central limit and other weak theorems 60J25 Continuous-time Markov processes on general state spaces 60J35 Transition functions, generators and resolvents

Zbl 0588.60058
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### References:

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