On martingale approximations

On Martingale Approximations

Consider additive functionals of a Markov chain Wk , with stationary (marginal) distribution and transition function denoted by π and Q, say Sn = g(W1) + · · · + g(Wn), where g is square integrable and has mean 0 with respect to π . If Sn has the form Sn =Mn + Rn, where Mn is a square integrable martingale with stationary increments and E(R2 n) = o(n), then g is said to admit a martingale appro...

Martingale Approximations for Sums of Stationary Processes

Approximations to sums of stationary and ergodic sequences by martingales are investigated. Necessary and sufficient conditions for such sums to be asymptotically normal conditionally given the past up to time 0 are obtained. It is first shown that a martingale approximation is necessary for such normality and then that the sums are asymptotically normal if and only if the approximating marting...

A ug 2 00 7 On Martingale Approximations ∗

Abstract Consider additive functionals of a Markov chain Wk, with stationary (marginal) distribution and transition function denoted by π and Q, say Sn = g(W1) + · · ·+ g(Wn), where g is square integrable and has mean 0 with respect to π. If Sn has the form Sn = Mn + Rn, where Mn is a square integrable martingale with stationary increments and E(R 2 n) = o(n), then g is said to admit a martinga...

Notes on Martingale Theory

On the Minimal Martingale Measureand