Abstract
We introduce a new set of Reciprocal Characteristics for the class of reciprocal diffusions naturally associated to a general parabolic second-order linear differential operator. All the coefficients of this operator, including the diffusion matrix, depend on time. This set of reciprocal characteristics is provided by the study of the symmetries of the differential operator. The Riemannian metric defined by the diffusion matrix is of central importance. Our reciprocal characteristics are the natural extension of Ovsiannikov's differential invariants to the time dependent parabolic case. We also show that the symmetries of the PDE coincide with the one parameter families of transformations which leave the usual stochastic Lagrangian as well as a modified Onsager–Machlup Lagrangian invariant.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
