A note on expected hitting times for birth and death chains (Q1126106)

A reversible Markov random walk on a locally finite graph is considered. A one step transition from a knot \(i\) to a knot \(j\) is possible (i.e. \(p_{ij}\neq 0\)) iff they are connected with an edge. Formulae for conditional expectations of a hitting time of the state \(j\) given an initial point \(i\) both for the finite and the infinite graph are derived. These formulae are interpreted in terms of electrical resistances inserted between knots in accordance with transition probabilities.