Expressions are developed for the moments of age and remaining life in renewal processes, and from them, expressions for the moments of the last and next renewal epochs. The results for remaining life and next renewal epoch may be regarded as generalizations of theorems of Wald (1944) and others. The results for age and last renewal epoch do not fit into this sequential analysis framework. Both sets of results are obtained from partial differential equations developed for the distributions of age and of remaining life. These partial differential equations are of the “conservation” type familiar from statistical mechanics, and may have some independent interest for renewal theory.
Expressions are developed for the moments of age and remaining life in renewal processes, and from them, expressions for the moments of the last and next renewal epochs. The results for remaining life and next renewal epoch may be regarded as generalizations of theorems of Wald (1944) and others. The results for age and last renewal epoch do not fit into this sequential analysis framework. Both sets of results are obtained from partial differential equations developed for the distributions of age and of remaining life. These partial differential equations are of the “conservation” type familiar from statistical mechanics, and may have some independent interest for renewal theory.
Computing rates of Markov models of voltage-gated ion channels by inverting partial differential equations governing the probability density functions of the conducting and non-conducting states