On the mean duration of random walks
Wolfgang R. Wasow · Journal of research of the National Bureau of Standards · 1951
The mean durat ion o f a di scr ete random walk in a bo unded domain is studied for general t ransition probabili ty fun ctio ns.The mean duration sat is fies an integral equation which, for small m ean step length, can b e approx imated by an ellipt ic differe nt ial equatio n.This leads to expli cit inequali t ies for the mean d uration in an important sp ecial case.