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Fokker-Planck equations describe time evolution of probability densities ofstochastic dynamical systems and play an important role in quantifyingpropagation and evolution of uncertainty. Although Fokker-Planck equations canbe written explicitly for nonlinear dynamical systems excited by Gaussian whitenoise, they are not available in general for nonlinear dynamical systemsexcited by multiplicative non-Gaussian white noise. Marcus stochasticdifferential equations are often appropriate models in engineering and physicsfor stochastic dynamical systems excited by non-Gaussian white noise. In thispaper, we derive explicit forms of Fokker-Planck equations for one dimensionalsystems modeled by Marcus stochastic differential equations undermultiplicative non-Gaussian white noise. As examples to illustrate thetheoretical results, the derived formula is used to obtain Fokker-Plankequations for nonlinear dynamical systems under excitation of (i)$\alpha$-stable white noise; (ii) combined Gaussian and Poisson white noise,respectively.

Derivation of Fokker-Planck equations for stochastic dynamical systems under excitation of multiplicative non-Gaussian white noise