For each gene, we characterised the distribution of sequence convergence between pairs of branches in the species phylogeny following the approach described by Castoe et al. (2009) implemented in the ...

Given a decreasing sequence {aⁿ} of nonnegative terms, we prove that there exist subsequences {nk } of {n} such that ∑k=1∞nk+1−nkank and ∑n=1∞an have the same convergence. In particular, ∑n=1∞an ...

This is a preview. Log in through your library . Abstract In this paper we establish maximal inequalities for ρ-mixing sequences and, as a consequence, we obtain the convergence of the expected value ...