A kinetic theory is developed for exonuclease-deficient DNA polymerases, based on the experimental observation that the rates depend not only on the newly incorporated nucleotide, but also on the previous one, leading to the growth of Markovian DNA sequences from a Bernoullian template. The dependences on nucleotide concentrations and template sequence are explicitly taken into account. In this framework, the kinetic and thermodynamic properties of DNA replication, in particular, the mean growth velocity, the error probability, and the entropy production in terms of the rate constants and the concentrations are calculated analytically. Theory is compared with numerical simulations for the DNA polymerases of T7 viruses and human mitochondria.