Strassen's invariance principle for additive functionals of Markov chains with spectral gap in the Wasserstein metric is proved.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-1-3, author = {W. Bo\l t and A. A. Majewski and T. Szarek}, title = {An invariance principle for the law of the iterated logarithm for some Markov chains}, journal = {Studia Mathematica}, volume = {209}, year = {2012}, pages = {41-53}, zbl = {1280.60043}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-1-3} }
W. Bołt; A. A. Majewski; T. Szarek. An invariance principle for the law of the iterated logarithm for some Markov chains. Studia Mathematica, Tome 209 (2012) pp. 41-53. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm212-1-3/