Martingale approximations for continuous-time and discrete-time stationary Markov processes

Hajo Holzmann

Stochastic Processes and their Applications, 2005, vol. 115, issue 9, 1518-1529

Abstract: We show that the method of Kipnis and Varadhan [Comm. Math. Phys. 104 (1986) 1-19] 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.

Keywords: Markov; process; Central; limit; theorem; Martingale; Moving; average; process; Normal; operator (search for similar items in EconPapers)
Date: 2005
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