Calculating Infinitesimal Generators

Ito’s lemma is a standard approach for calculating infinitesimal generators for stochastic process models. We present alternate ad-hoc methods based on elementary calculations for many commonly considered stochastic models. The only tools that we employ are binomial expansion, Taylor series expansion and solution methods for elementary differential equations. Our alternate approaches are especially useful for processes which cannot be expressed as stochastic differential equations, for which Ito’s lemma cannot be applied.