A note on a derivation method for SDE models: Applications in biology and viability criteria

Abstract

We discuss a method, which was popularized by E. J. Allen and that is frequently used in applications to construct SDE models. The derivation procedure is based on information about the elementary processes involved in the dynamics and their corresponding probabilities. We formulate criteria for the viability of the resulting models. In particular, explicit necessary and sufficient conditions are deduced for the non-negativity and/or boundedness of solutions. Moreover, we show that the class of deterministic models for which the construction leads to an admissible SDE extension is strongly limited. Several examples are presented to illustrate the implications of our results.