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Rates of convergence in the strong invariance principle under projective criteria

   
@article{EJP1849,
	author = {Jérôme Dedecker and Paul Doukhan and Florence Merlevède},
	title = {Rates of convergence in the strong invariance principle under projective criteria},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {17},
	year = {2012},
	keywords = {almost sure invariance principle ; strong approximations ; weak dependence ;  Markov chains},
	abstract = { 
We give rates of convergence in the strong invariance principle for stationary  sequences satisfying some projective criteria. The conditions are expressed in terms  of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some  applications to a reversible Markov chain, to symmetric random walks on the circle, and to functions of dependent sequences.
},
	pages = {no. 16, 1-31},
	issn = {1083-6489},
	doi = {10.1214/EJP.v17-1849},    
        url = {http://ejp.ejpecp.org/article/view/1849}}