Some Markov chains on abelian groups with applications [chapter]

Vadim A. Kaimanovich
2004 Random Walks and Geometry  
We study the central limit theorem and the structure of the corresponding covariance operator for the Markov chains generated by successive (overlapping) k-tuples (X n+1 , . . . , X n+k ), n = 0, 1, . . . formed from the i.i.d.r.v. {X n }. The potential application of the theory includes the design of statistical tests. In particular, we present the explicit spectral analysis of the covariance matrices related to Marsaglia's k permutation test for k = 2, 3, 4, 5.
doi:10.1515/9783110198089.1.3 fatcat:uqfukthrhvh3vdzupuaenjplwi