Relations between Markov Processes via Local Time and Coordinate Transformations

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Abstract
The Duru-Kleinert method of solving unknown path integrals of quantum mechanical systems by relating them to known ones does not apply to Markov processes since the Duru-Kleinert transform of a Fokker-Planck equation is, in general, not a Fokker-Planck equation. In this Letter, 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-Brand process.