Monotone measures of ergodicity for Markov chains (Q1271246)

A finite homogeneous continuous-time ergodic Markov chain is considered, \(\pi =( \pi _n) \) is its stationary distribution and the initial state probabilities \(p_n(0)\neq \pi _n.\) The authors prove that the function \(q_\alpha (t)=\left\{ \sum p_n(t)(p_n(t)/\pi_n) ^\alpha \right\} ^{1/\alpha }(\alpha \neq 0),\;q_0(t)=\sum p_n(t)\log (p_n(t)/\pi_n))\) is stricly decreasing if \(\alpha >-1 \) and is stricly increasing if \(\alpha <-1\).