We introduce and study conditional differential equations, a kind of random differential equations. We give necessary and sufficient conditions for the existence of a solution of such an equation. We apply our main result to a Malthus type model.
Nel panorama della scienza contemporanea, la biologia molecolare ha recentemente assunto un ruolo di fondamentale importanza. Il bisognocrescente di conoscere intere sequenze genomiche e l’esigenza, ancora piùpressante, di analizzare e confrontare tali sequenze per poter dedurre funzionalità e discendenze comuni, ha reso necessaria l’integrazione delleusuali tecniche sperimentali, proprie della ricerca biologica, con le metodologie formali della matematica e dell’informatica. Queste motivazioni...
Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence...