Integrable Ito equations with multiple noises

Abstract

The classification of scalar Ito equations with a single noise source which admit a so called standard symmetry and hence are -- by the Kozlov construction -- integrable is by now complete. In this paper we study the situation, occurring in physical as well as biological applications, where there are two independent noise sources. We determine all such autonomous Ito equations admitting a standard symmetry; we then integrate them by means of the Kozlov construction. We also consider the case of three or more independent noises, showing no standard symmetry is present.