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.

32 pages, no figures. V3 is the published version

References in corpus (5)

• Symmetry of stochastic non-variational differential equations
• W-Symmetries of Ito stochastic differential equations
• Integration of the stochastic logistic equation via symmetry analysis
• Symmetry classification of scalar autonomous Ito stochastic differential equations with simple noise
• Symmetry of the isotropic Ornstein-Uhlenbeck process in a force field

Cited by in corpus (1)

• On the integration of Ito equations with a random or a W-symmetry