Relations Between Markov Processes Via Local Time and Coordinate Transformations
arXiv:cond-mat/9608120 · doi:10.1103/PhysRevLett.78.565
Abstract
The Duru-Kleinert (DK) method of solving unknown path integrals of quantum mechanical systems by relating them to known ones does not apply to Markov processes since the DK-transform of a Fokker-Planck equation is in general not a Fokker-Planck equation. In this note, we present a significant modification of the method, based again on a combination of path-dependent time and coordinate transformations, to obtain such relations after all. As an application we express unknown Green functions for a one-parameter family of Markov processes in terms of the known one for the Schenzle-Brandt process.
Final version to appear in Phys. Rev. Letters. Author Information under http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at http://www.physik.fu-berlin.de/~kleinert/kleiner_re/preprint.html