A formal approach for handling lie point symmetries of scalar first-order ito stochastic ordinary differential equations

Abstract

Many methods of deriving Lie point symmetries for Itô stochastic ordinary differential equations (SODEs) have surfaced. In the Itô calculus context both the formal and intuitive understanding of how to construct these symmetries has led to seemingly disparate results. The impact of Lie point symmetries on the stock market, population growth and weather SODE models, for example will not be understood until these varying results are reconciled as has been attempted here.