Stochastic mechanics and Feynman path integrals

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Abstract
A relation between the kernel of a quantum system in Feynman’s path-integral theory and the transition probability of the corresponding Markov process, with the diffusion coefficient rotated to the imaginary axis, is obtained in the framework of stochastic mechanics. If a stationary state is considered, the relation reduces to a form relating a Euclidean (i.e., imaginary time) quantum theory to a Markov process.