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In this paper pseudo-differential operators with negative definite symbolsare used to construct time- and space-inhomogeneous Markov processes. This isachieved by using the Markov evolution system associated with the fundamentalsolution of the corresponding pseudo-differential evolution equation. Negativedefinite symbols are non-standard and differ significantly from the class ofH\"{o}rmander type symbols. The novelty of this work is the derivation and therepresentation of the fundamental solution as a Feynman path integral. Thisimplies that the transition function of the constructed Markov process can bewritten as a pseudo-differential operator that has a Feynman path integral asits symbol.

A Pseudo-Differential Operator Construction of Markov Processes Using Feynman Path Integrals