Distribution-Independent Generalization of the Feynman–Kac Formula

Determine whether a generalization of the Feynman–Kac formula that applies to symmetric Lévy flights and fractional operators can be formulated independently of both the underlying noise distribution family and the order of the differential operator, and, if such a formulation exists, explicitly derive it.

Background

The Feynman–Kac formula links stochastic processes to parabolic partial differential equations and has known extensions to symmetric Lévy flights and fractional operators. These extensions, however, often depend on specific distributional assumptions or operator orders.

The paper explicitly notes that it remains unresolved whether the Feynman–Kac generalization can be made independent of the distribution type and derivative order, posing a clear theoretical question about universality of the formulation.