Martingale approximations for continuous-time and discrete-time stationary Markov processes
نویسنده
چکیده
We show that the method of Kipnis and Varadhan (Comm. Math. Phys. 104 (1986) 1) 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: Primary 60F05, 60G44; Secondary 60J25, 60J35
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